Vijay Gupta



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  • Profile
  • QualificationsM.Sc., M. Phil., Ph. D.
  • DesignationProfessor
  • DivisionMathematics
  • Contact No.+91-11-2509906
  • E-Mailvijaygupta2001@hotmail.com

Biosketch

Dr. Vijay Gupta is a Professor of Mathematics and Ex. Head (2013-Feb 2018), Department of Mathematics, NSIT (now Netaji Subhas University of Technology), New Delhi. A PhD from University of Roorkee (now IIT Roorkee). His area of research interest is Approximation Theory, especially he works on linear positive operators. He is the author/co-author of Five books, Fifteen book chapters and over 300 research papers. He is also actively involved in editing several international scientific research journals, also he edited several books. The present h-index (as per google scholar) is 37

Areas of Interest

Approximation Theory

List of Publication

 

(i) Papers published in journals (314)

 

1.  M. Saleem, S.  U. Siddiqui  and Vijay Gupta, A mathematical model with young predation, J. Math. Biology 25 (1987), 89-101. ISSN: 0303-6812, IF 1.846

 

2. P. N. Agrawal, Vijay Gupta and A. Sahai, On convergence of derivatives of linear combinations of modified Lupas operators, Publ. Inst. Math. (Beograd) 45 (59) (1989), 147-154.ISSN 035 1302

 

3 Vijay Gupta and P. N. Agrawal, On linear combination of Phillips operators, Indian Acad. Math. 11(2) (1989), 106-114.

 

4. T. A. K. Sinha, P. N. Agrawal, A. Sahai and Vijay Gupta, Improved Lp approximation by linear combination of modified Lupas operators, Bull. Inst. Math. Acad Sinica 17 (3) (1989), 106-114.ISSN 2304 7909

 

5. P. N. Agrawal and Vijay Gupta, Simultaneous approximation by linear combination of modified Bernstein polynomials, Bull Greek Math. Soc. 39 (1989), 29-43. ISSN 0072-7466

 

6 Vijay Gupta, P. N. Agrawal, A. Sahai and T. A. K. Sinha, Lp-approximation by combination of modified Szasz-Mirakyan operators, Demonstratio Math. 23 (3) (1990), 577-591.ISSN 0420-1213

 

7. P. N. Agrawal and Vijay Gupta, On the iterative combination of Phillips operators, Bull. Inst. Math. Acad Sinica 18 (4) (1990), 361-368. ISSN 2304 7909

 

8.  Vijay Gupta and P. N. Agrawal, An estimate of the rate of convergence for modified Szasz-Mirakyan operators of functions of bounded variation, Publ. Inst. Math. (Beograd) 49 (63) (1991), 97-103. ISSN 035 1302

 

9.  R.P. Sinha, P. N. Agrawal, and Vijay Gupta, On simultaneous approximation by modified Baskakov operators, Bull. Soc. Math. Belg. Ser. B 43 (2) (1991), 217-231. ISSN 0037-9476

 

10.  H. S. Kasana, P. N. Agrawal and Vijay Gupta, Inverse and saturation theorems for linear combination of modified Baskakov operators, Approx Theory and its Appl. 7 (2) (1991), 65-81. ISSN 1672-4070

 

11. P. N. Agrawal and Vijay Gupta, A saturation theorem for linear combinations of Bernstein Durrmeyer polynomials, Ann Polonici  Math. LVII (2)  (1992), 157-164. ISSN 0066-2216

 

12. Vijay Gupta and P. N. Agrawal, Lp-approximation by iterative combination of Phillips operators, Publ. Inst. Math. (Beograd) 52 (66) (1992), 101-109. ISSN 035 1302

 

13. Vijay Gupta and Ashok Sahai, On linear combination of Phillips operators, Soochow J. Math. 19 (3) (1993), 313-323. 

 

14.  Vijay Gupta, A note on modified Szasz operators, Bull Inst. Math. Acad Sinica 21 (3) (1993), 275-278. ISSN 2304 7909

 

15.  Vijay Gupta and G. S. Srivastava, Simultaneous approximation by Baskakov-Szasz type operators, Bull. Math.de la  Soc. Sci. de Roumanie (N. S.) 37 (85)(3-4) (1993), 73-85. ISSN 1220-3874

 

16. P. N. Agrawal and Vijay Gupta, On convergence of derivatives of Phillips operators, Demonstratio Math. 27 (2) (1994), 501-510. 

 

17. Vijay Gupta, A note on modified Baskakov type operators, Approx Theory and its Appl. 10 (3) (1994), 74-78. ISSN 1672-4070

 

18. P. N. Agrawal and Vijay Gupta, Inverse theorem for linear combinations of modified Bernstein polynomials, Pure and Applied Math Sci. 40 (1995), 29-38. 

 

19. Vijay Gupta, G. S. Srivastava and T. A. K. Sinha, Inverse theorem in Lp-approximation by modified Szasz-Mirakyan operators, Demonstratio Math. 28 (2) (1995), 285-292. 

 

20. Vijay Gupta and G. S. Srivastava, Inverse theorem for Szasz Durrmeyer operators, Bull. Inst. Math. Acad Sinica 23 (2) (1995), 141-150. 

 

21. Vijay Gupta, G. S. Srivastava and A. Sahai, On simultaneous approximation by Szasz Beta operators, Soochow J. Math. 21 (1) (1995), 1-11. 

 

22. Vijay Gupta, Approximation by Szasz Durrmeyer operators, Ganita 46 (2) (1995), 65-72. 

 

23. Vijay Gupta and G. S. Srivastava, Convergence of derivatives by summation-integral type operators, Revista Colombiana de Mate. 29 (1) (1995), 1-11. 

 

24. Vijay Gupta, Global approximation by modified Baskakov type operators, Publ. Math. 39 (2) (1995), 263-271.

 

25. Vijay Gupta and A. Ahmad, Simultaneous approximation by modified Beta operators, Istanbul Universitesi Fen Fakultesi Mat Dergsi 54 (1995), 11-22.

 

26. Vijay Gupta, A sharp estimate on the degree of approximation to functions of bounded variation by certain operators, Approx. Theory and its Appl. 11:3(1995), 106-107. 

 

27. Vijay Gupta, Simultaneous approximation by Szasz-Durrmeyer operators, The Math. Student 64, 1-4 (1995), 27-36. 

 

28. Vijay Gupta and A. Ahmad, An improved estimate on the degree of approximation to function of bounded variation by certain operators, Revista Colombiana de Mate. 29 (2) (1995), 119-126. 

 

29. Vijay Gupta and G. S. Srivastava, On convergence of derivatives by Szasz-Mirakyan-Baskakov type operators, The Math Student 64 (1-4) (1995), 195-205. 

 

30. Vijay Gupta, Rate of convergence by Baskakov Beta operators, Mathematica 37 (60) (1-2) (1995), 109-117. 

 

31. Vijay Gupta and G. S. Srivastava, Saturation theorem for Szasz Durrmeyer operators, Demonstratio Math. 29 (1) (1996), 7-16. 

 

32. Vijay Gupta and G. S. Srivastava, An estimate on the rate of convergence of modified Baskakov operators for functions of bounded variation, Kyungpook Math. J. 36 (1996), 237-247. 

 

33. Vijay Gupta, On the rate of pointwise convergence of modified Baskakov operators, Soochow Math. J. 22 (4) (1996), 543-552. 

 

34. Vijay Gupta and G. S. Srivastava, Approximation by Durrmeyer type operators, Ann.  Polonici Math. LXIV, 2 (1996), 153-159. 

 

35. Vijay Gupta and Paulina Pych Taberska, On the rate of point wise convergence of modified Baskakov operators, Functions et Approximatio XXIV (1996), 59-67. 

 

36.  Vijay Gupta, A note on modified Bernstein polynomials, Pure and Applied Math Sci.  44  (1-2) (1996), 1-3. 

 

37. Vijay Gupta and G. S. Srivastava, On the rate of convergence of Phillips operators for functions of bounded variation, Commentation Math. XXXVI (1996), 123-130.

 

38. Vijay Gupta and P. N. Agrawal, Inverse theorem in simultaneous approximation by Szasz Durrmeyer operators, J. Indian Math. Soc. 63(1-4) (1997), 99-113. 

 

39. Vijay Gupta and G. S. Srivastava, On simultaneous approximation by combinations of Baskakov-Szasz type operators, Fasciculi Mate. 27(1997), 29-42. 

 

40. Vijay Gupta and D. Kumar,  Rate of convergence for  modified Baskakov operators, Demonstratio Math XXX (2) (1997), 339-346. 

 

41.Vijay Gupta and G. S. Srivastava, Saturation theorem in Lp-approximation by combinations of modified Szasz-Mirakyan operators, Demonstratio Math. 30 (3)(1997),573-578. 

 

42. Vijay Gupta, A note on the rate of convergence of Durrmeyer operators for functions of bounded variation, Soochow J. Math. 23 (1)(1997), 117-120. 

 

43. Vijay Gupta and K. V. Arya, On the rate of point wise convergence of modified Baskakov type operators for functions of bounded variation, Kyungpook Math. J. 38 (2) (1998), 307-315. 

 

44. G. S. Srivastava and Vijay Gupta, Converse theorem for modified Baskakov type operators, Istanbul Universitesi Fen Fakultesi Mat Dergsi 57-58 (1998-1999), 63-69.

 

45. Vijay Gupta and Prabhakar Gupta, Rate of convergence by Szasz-Mirakyan Baskakov type operators, Istanbul Universitesi Fen Fakultesi Mat. Dergisi 57-58 (1998-1999), 71-78.

 

46. Vijay Gupta and D. Kumar, On approximation by Lagrange’s interpolation polynomials, Pan American Math. J. 9 (4) (1999), 69-82.

 

47. Vijay Gupta and R. P. Pant, Rate of convergence of the modified Szasz-Mirakyan operators on functions of bounded variation, J. Mathematical Analysis and Applications 233 (1999), 476-483. 

 

48. Vijay Gupta, Prabhakar Gupta and Marc Rogalski, Improved rate of convergence for the modified Szasz-Mirakyan operators, Approx. Theory and its Appl. 16:3(2000), 94-99. 

 

49. Prabhakar Gupta and Vijay Gupta, Rate of convergence on Baskakov-Szasz type operators, Fasciculi Mate. 31 (2001), 37-44. 

 

50. Vijay Gupta and Prabhakar Gupta, Direct theorem in simultaneous approximation for  Szasz-Mirakyan Baskakov type operators, Kyungpook Math. J. 41 (2) (2001), 243-249. 

 

51. R. P. Pant, P.C. Joshi and Vijay Gupta, A Meir Keeler type fixed point theorem, Indian J. Pure and Appl. Math.32(6) (2001), 779-787.ISSN 0019-5588 IF 0.224

 

52. Vijay Gupta and Prabhakar Gupta, Rate of convergence for the Baskakov-Durrmeyer type operators, Ganita 52 (1) (2001), 69-77. 

 

53. Vijay Gupta, Prabhakar Gupta and P. N. Agrawal, Saturation theorem in simultaneous approximation by Szasz Durrmeyer, J. Indian Math. Soc. 69 ,(1-4) (2002), 65-69. 

 

54.   Vijay Gupta, On a new type of Meyer Konig and Zeller operators, J. Inequal. Pure Applied Math. 3 (4) (2002) Art. 57.

 

55. Vijay Gupta, A note on Meyer Konig and Zeller operators for functions of bounded variation, Approx. Theory and its Appl. 18 (3) (2002), 99-102. 

 

56. Vijay Gupta, Rate of convergence on Baskakov Beta Bezier operators for functions of bounded variation, Int.  J.   Math. and  Math. Sci. 32 (8) (2002), 471-479.

 

57. Vijay Gupta, Inequality estimate on Durrmeyer type operators, J. Nonlinear Functional Analysis and Applications, 7 (4) (2002), 481-494.

 

58. X. M. Zeng and Vijay Gupta, Rate of convergence of Baskakov-Bézier type operators for locally bounded functions, Comput. Math. Appl.44 (10-11) (2002), 1445-1453. 

 

59. Vijay Gupta, V. Vasishtha and M. K. Gupta, Rate of convergence of the Szasz-Kantorovitch-Bezier operators, Publications de l' Inst. Math. 72(86) (2002), 137-143.

 

60.  Ulrich Abel, Vijay Gupta and M. Ivan, On the rate of convergence of bounded variation functions by Baskakov-Kantorovitch-Bezier operators, Revue D’Anal. Numerique et de Theorie de L’ Approximation 31(2) (2002), 123-133.

 

61. Ulrich Abel and Vijay Gupta, An estimate of the rate of convergence of a Bézier variant of the Baskakov-Kantorovich operators for bounded variation functions, Demons. Math. 36(1) (2003), 123-136. 

 

62.Ulrich Abel, Vijay Gupta and M. Ivan, On the rate of convergence of a Durrmeyer variant of Meyer Konig and Zeller operators, Archieves Inequal. Appl. 1(2003), 1-9.

 

63. Vijay Gupta, Prerna Maheshwari and V. K. Jain, Lp Inverse theorem for modified Beta operators, Int. J. Math. Math. Sci. 33 (20) (2003), 1395-1403.

 

64. Vijay Gupta and Niraj Kumar, A note on the integral modification of the Meyer Konig and Zeller operators, Int.  J. Math. and   Math. Sci. 2003:31 (2003), 2003-2009.

 

65. H. M. Srivastava and Vijay Gupta, A certain family of summation integral type operators, Math and Comput. Modelling 37 (2003), 1307-1315.

 

66. Vijay Gupta, Rate of approximation by new sequence of linear positive operators, Comput. Math. Appl. 45(12) (2003), 1895-1904.

 

67. Vijay Gupta, V. Vasishtha and M. K. Gupta, Rate of convergence of summation-integral type operators with derivatives of bounded variation, J Inequqlities in Pure and Applied Mathematics 4(2) (2003), Art.34. 

 

68. Vijay Gupta and Ulrich Abel, On the rate of convergence of Bezier variant of Szasz-Durrmeyer operators, Analysis in Theory and Applications 19:1 (2003), 81-88. 

 

69. Vijay Gupta and Prerna Maheshwari, Bezier variant of a new Durrmeyer type operators, Rivista di Matematica della Università di Parma" volume 7 (2) (2003), 9-21.

 

70. Vijay Gupta, Prerna Maheshwari and V. K. Jain, On the linear combinations of modified Beta operators, Pure and Applied Math Sci. 48 (2003),

 

71. Vijay Gupta and Prerna Maheshwari, On Baskakov Szasz type operators, Kyungpook Math. J. 43(3)   (2003), 315-325.

 

72. Prerna Maheshwari and Vijay Gupta, An estimate on the rate of convergence for modified Beta operators, Indian J. Pure and Appl. Math. 34 (2003). 

 

73. Vijay Gupta, V. Vasishtha and M. K. Gupta, An estimate on the rate of convergence of Bezier type summation integral operators, Kyungpook Math. J. 43 (2003), 345-354.

 

74. Vijay Gupta, M. K. Gupta and V. Vasishtha, Simultaneous approximation by summation integral type operators, J. Nonlinear Functional Analysis and Applications, 8(3) (2003), 399-412.

 

75. Ulrich Abel, Vijay Gupta and Mircea Ivan, The complete asymptotic expansion for   Baskakov Szasz Durrmeyer operators, Annals Tiberiu Popoviciu Itinerant Seminar of Functional Equations, Approximation and Convexity, , Vol. 1 (2003) 3-15.

 

76. Vijay Gupta, Degree of approximation to function of bounded variation by Bezier variant of MKZ operators, J. Mathematical Analysis and Applications. 289 (1) (2004), 292-300. 

 

77.  Vijay Gupta, Rate of convergence by Bezier variant of Phillips operators, Taiwanese J. Math.8 (2) (2004), 183-190.

 

78. Vijay Gupta, The Bezier variant of Kantorovitch operators, Comput. Math. Appl. 47 2/3 (2004), 227-232. 

 

79. Vijay Gupta and Ulrich Abel, Rate of convergence of bounded variation function by a Bezier Durrmeyer variant of Baskakov operators, International J. Math and Math Sci. 2004 (9)(2004), 459-468.

 

80. Vijay Gupta and M. K. Gupta, Rate of convergence for certain family of summation integral type operators, J. Math. Anal. Appl. 296 2 (2004), 608-618. 

 

81. Vijay Gupta, Rate of convergence of Baskakov-Beta Bezier operators for locally bounded functions, Turkish J. Math.28 (3) (2004), 271-280.

 

82. U. Abel and V. Gupta, Rate of convergence of Stancu beta operators for functions   of   bounded variation, Revue D’Anal. Numerique et de Theorie de L’ Approximation 33(1) (2004), 3-9.

 

83. Vijay Gupta and Ulrich Abel, The rate of convergence by a new type of Meyer Konig and Zeller operators, Fasciculi Math. 34 (2004), 15-23.

 

84. Ulrich Abel, Vijay Gupta and M. Ivan, The complete asymptotic expansion for general Durrmeyer variant of Meyer Konig and Zeller operators,  Mathematical and Computer Modelling 40 (2004), 867-875

 

85.Vijay Gupta and N. Ispir, On simultaneous approximation for some Bernstein type operators, International J. Math and Math Sci. 2004 (71)(2004), 3951-3958.

 

86. Vijay Gupta and Alexandru Lupas, On the rate of approximation for the Bezier variant of Kantorovich-Balasz operators, General Mathematics, 12 (3) (2004), 3-18.

 

87. Jesus de la Cal and Vijay Gupta, On the approximation of locally bounded functions by operators of Bliemann Butzer and Hahn, J. Inequal Pure Appl. Math. 6 (1) (2005), Art 4, 1-10.

 

88. Vijay Gupta and Ogun Dogru, Direct results for certain family of integral type operators, J. Inequal Pure Appl. Math. 6 (1) (2005), Art 21, 1-11.

 

89. Ulrich Abel, Vijay Gupta and M. Ivan, Rate of convergence of Kantorovitch variant of Meyer-Konig Zeller operators, Mathematical Inequality and Applications 8 (1)(2005).

 

90. Vijay Gupta, Some approximation properties for modified Baskakov type operators, Georgian Math. J.  12 (2)  (2005), 217-228.

 

91. Z. Finta and Vijay Gupta, Direct and inverse estimates for Phillips type operators, J. Math Anal Appl. 303(2) (2005), 627-642. 

 

92. Ulrich Abel, Vijay Gupta and Ram N. Mohapatra, Local approximation by beta operators, Nonlinear Analysis, Series A, Theory and Methods 62 (1) (2005), 41-52.

 

93. H. M. Srivastava and Vijay Gupta, Rate of convergence for Bezier variant of the Bleimann-Butzer-Hahn operators, Applied Mathematics Letters 18 (8) (2005), 849-857.

 

94.  Ogun Dogru and Vijay Gupta, Motonocity and asymptotic estimate of Bleiman Butzer and Hahn operators based on q-integers, Georgian Math. J. 12 3 (2005), 415-422.

 

95. Vijay Gupta and N. Ispir, On the Bezier variant of  generalized Kantorovitch type Balazs operators, Applied Mathematics Letters 18(9) (2005),  1053-1061.

 

96. Ulrich Abel, Vijay Gupta and M. Ivan, Asymptotic approximation of functions and their derivatives by generalized Baskakov-Szasz-Durrmeyer operators, Analysis in Theory and Application 21 (1) (2005), 15-26.

 

97. Vijay Gupta and Alexandru Lupas, Rate of Approximation for the Bezier variant of Bleimann-Butzer  and Hahn operators, General Mathematics 13 (1) (2005), 41-54.

 

98. Vijay Gupta and Alexandru Lupas, Direct results for mixed Beta Szasz type operators, General Mathematics 13 (2) (2005), 83-94.

 

99. Vijay Gupta and N Deo, On the rate of convergence for bivariate Beta operators, General Mathematics 13 (3) (2005), 107-114. 

 

100. Vijay Gupta R. N. Mohapatra and Z. Finta, On certain family of mixed summation integral type operators, Mathematical and Computer Modelling 42 (2005), 181-191.

 

101. Vijay Gupta, An Estimate on the convergence of Baskakov Bézier operators, J Mathematical Analysis and Applications 3121 (2005), 280-288. ISSN 0022-247X IF 1.204

 

102. Vijay Gupta, Ulrich Abel and M. Ivan, Rate of convergence of Beta operators of second kind for functions with derivatives of bounded variation, International Journal of Math and Math Sci. 2005(23) (2005), 3827-3833.

 

103. Vijay Gupta, Rate of convergence for Szasz Bézier operators, Ukrianian Mathematical Journal 57 (12) (2005), 1892-1900.

 

104. Z. Finta and Vijay Gupta, Some direct results for the iterative combinations of Stancu beta operators, J. Concrete and Applicable Mathematics 4(2) (2006), 229-240.

 

105. Vijay Gupta, Error estimation by mixed summation integral type operators, J. Mathematical Analysis and Applications  313 2 (2006), 632-641.

 

106. Vijay Gupta and N. Ispir, On the Kantorovitch variant of generalized Bernstein type rational functions, Demons. Math. 39 1 (2006), 117-130. ISSN 0420-1213

 

107. Vijay Gupta and Esra Erkus, On certain hybrid family of summation integral type operators, Journal of Inequalities in Pure and Applied Mathematics 7 (1) (2006), 1-11. 

 

108. Vijay Gupta and Ogun Dogru, Approximation of bounded variation functions by a Bezier variant of the  Beilmann, Butzer and Hahn operators, International J.  Math Math Sci Vol. 2006, Art Id 37253, (2006), 1-5.

 

109. V. Gupta and R. N. Mohapatra, On the rate of convergence for certain summation integral type operators, Mathematical Inequalities and Applications 9 (3) (2006), 465-472. 

 

110. Ogun Dogru and Vijay Gupta, Korovkin type approximation properties of bivariate q-Meyer Konig and Zeller operators, Calcolo 43(1)(2006), 51-63.

 

111. Vijay Gupta, Tengiz Shriayev  and M. Craciun, Rate of approximation for certain Durrmeyer operators. Georgian Math J. 13 (2) (2006), 277-284.

 

112. Vijay Gupta and M A Noor, Convergence of derivatives for certain mixed Szasz Beta operators, Journal of   Mathematical  Analysis and  Applications 321 (1) (2006), 1-9.  

 

113. A. Aral and Vijay Gupta, q-derivatives and applications to the q-Szasz Mirakyan operators, Calcalo 43 (3) (2006), 151-170.

 

114. Vijay Gupta, M. A. Noor and M. S. Beniwal, Rate of convergence in simultaneous approximation for Szasz Mirakyan Durrmeyer operators, Journal of Mathematical Analysis and Applications 322 (2) (2006), 964-970. 

 

115. O. Duman, E. Erkus and V. Gupta, Statistical Rates on The Multivariate Approximation Theory, Math Comput Modelling 44 (9-10) (2006), 763-770.

 

116. N K Govil and V Gupta, Simultaneous approximation for Bezier variant of Baskakov Beta operators, Mathematical and Computer Modelling 44, 11-12(2006), 1153-1159.

 

117. N K Govil, Vijay Gupta and M A Noor, Simultaneous approximation for the Phillips operators, International Journal of Math and Math Sci. Vol. 2006 Art Id. 49094 (2006), 1-9.

 

118. Vijay Gupta, M A Noor, Man Singh Beniwal and M K Gupta, On simultaneous approximation for certain Baskakov Durrmeyer type operators. Journal of Inequalities in Pure and Applied Mathematics 7 (4) (2006), Art.125, 1-15.

 

119. Vijay Gupta, P. N. Agrawal and H. Karsi, Simultaneous Approximation for the  Phillips Bezier Operators, Journal of Inequalities in Pure and Applied Mathematics 7 (4) (2006), 1-15.

 

120. N K Govil and Vijay Gupta, Rate of convergence for Baskakov type operators on functions of bounded variation, Journal of Combinatorics, Information and System Sciences 31 (1-4) (2006), 1-17.

 

121. Zoltan Finta, N K Govil and V. Gupta, Some results on modified Szasz-Mirakyan operators, Journal of Mathematical Analysis and Applications 327(2)(2007), 1284-1296.

 

122.Vijay Gupta, Simultaneous approximation for Bezier variant of Szasz-Mirakyan- Durrmeyer operators, Journal of Mathematical Analysis and Applications 328(1) (2007),101-105. ISSN 0022-247X IF 1.204

 

123. Vijay Gupta and R. N. Mohapatra, Rate of convergence for modified Szasz operators, Journal of Concrete and Applicable Mathematics 5(3) (2007), 197-202.

 

124. M K Gupta, Vijay Gupta and Manoj Kumar, Direct and inverse estimates for a new family of linear positive operators in simultaneous approximation, J. Math Anal Appl 320 (2) (2007), 799-816. 

 

125. N K Govil and V Gupta, Direct estimates in simultaneous approximation for Durrmeyer type operators, Mathematical Inequalities and Applications 10 (2) (2007), 371-379. 

 

126. Vijay Gupta and P. N Agrawal, Rate of convergence for certain Baskakov Durrmeyer type operators, Anal. Univ. Ordea Fasc. Math. 14 (2007), 33-39. 

 

127. H. M. Srivastava, Zoltan Finta and Vijay Gupta, Convergence of a certain family of summation integral type operators, Applied Mathematics and Computation 190 (2007),449-457. 

 

128. Vijay Gupta, On bounded variation functions by a general MKZD operators, Acta Mathematica Sinica, Eng. Ser. 23 (8) (2007), 1457-1462.

 

129. M A Noor and Vijay Gupta, Modified Householder iterative method free from second derivatives for nonlinear equations, Applied Mathematics and Computation, 190 (2) (2007), 1701-1706. 

 

130. Vijay Gupta and X. M. Zeng, On the Bezier variant of Balazs Kantorovitch operators, Math Slovaca  57 (4) (2007), 349-358.

 

131. Vijay Gupta, Erratum to "Simultaneous approximation for Bezier variant of Szasz-Mirakyan-Durrmeyer operators "[J. Math. Anal. Appl. 328 (2007) 101-105]”, J.  Math Anal. Appl. 335 (2)(2007), 1485. 

 

132.  M. A. Noor, Khalida Inayat Noor and Vijay Gupta, On equilibrium like problems, Applicable Analysis, Applicable Analysis 86(7)(2007), 807-818. 

 

133. Z. Walczak and Vijay Gupta, Uniform convergence with certain linear operators, Indian J. Pure and Applied Math. 38 (2007), 259-269. 

 

134. Vijay Gupta and Harun Karsi, Rate of convergence for Bezier variant of MKZD operators, Georgian Math J. 14 (4)(2007), 651-659. 

 

135. Xu Chen, Xioming Zeng, Lian Boyong and Vijay Gupta, Convergence Property of Control Meshes of Catmull-Clark Surfaces, Journal of Mathematical Study, 40 (2007), 386-391.  

 

136.Vijay Gupta and Jyoti Sinha, Simultaneous approximation for generalized Baskakov-Durrmeyer type operators, Mediterranean Journal of Mathematics 4 (4) (2007), 483-495. 

 

137. P. N. Agrawal, Vijay Gupta and Asha Ram Gairola, On the derivatives of iterative combinations of Phillips operators, Nonlinear Funct. Anal. Appl. 12 (2) (2007), 195-203.

 

138. Harun Karsli and Vijay Gupta, On Convergence of q-Chlodowsky operators, Applied Mathematics and Computation 195 (1) (2008), 220-229. 

 

139. Vijay Gupta and Jyoti Sinha, Direct results on certain Szasz-Mirkyan operators, Applied Mathematics and Computation 195 (1) (2008), 230-239. 

 

140. Vijay Gupta, Some approximation properties on q-Durrmeyer operators, Applied Math Computation 197 (1) (2008), 172-178.

 

141. Nurhayat Ispir and Vijay Gupta, A Statistical approximation by generalized Kantorovich Bernstein type rational operators, South East Asian Bull of Math. 32 (1) (2008), 87-98.      

 

142. Vijay Gupta and Mircea Ivan, Rate of simultaneous approximation for the Bezier variant of certain operators, Applied Mathematics and Computation 199 (1) (2008), 392-395. 

 

143. Ulrich Abel, Vijay Gupta and Ram N. Mohapatra, Local approximation by a variant of  Bernstein Durrmeyer operators, Nonlinear Analysis Series A: Theory, Methods & Applications 68 (11) (2008), 3372-3381. 

 

144. H. Karsi and Vijay Gupta,  Rate of Convergence by Nonlinear Integral Operators for Functions of Bounded Variation, Calcolo 45 (2008), 87-97.  

 

145. Vijay Gupta, Rate of approximation for the Balazs-Kantorovich-Bezier operators, Applied Mathematics and Computation 199 (2) (2008),  823-827

 

146. Vijay Gupta and R. N. Mohapatra, Approximation by Durrmeyer Bezier operators, Nonlinear Analysis, Ser. B, Real World Applications 9 (4) (2008), 1491-1498.

 

147. Z. Walczak and V Gupta, A Note on the convergence of Baskakov type operators, Applied Mathematics and Computation 202(1) (2008), 370-375. 

 

148. Vijay Gupta and H Wang, The rate of convergence of q-Durrmeyer operators for 0<q<1. Mathematical Methods in Applied Sciences 31 (16) (2008), 1946-1955.

 

149. Zoltan Finta and Vijay Gupta, Durrmeyer type Generalized Baskakov-Beta Operators, South East Asian Bull. Math. 32(6) (2008), 1037-1048.   

 

150. N. K. Govil and Vijay Gupta, Convergence rate for generalized Baskakov type operators, Nonlinear Analysis Series A: Theory, Methods & Applications, 69, Issue 11, 1 December (2008)  3795-3801.

 

151. P. N. Agrawal, Vijay Gupta and Asha Ram Gairola, On iterative combination of a Bernstein Durrmeyer-type operators, Georgian Mathematical J 15(4) (2008), 591-600.

 

152. Vijay Gupta, Rate of convergence for generalized Baskakov Beta operators, South East Asian Bull. Math. 33 (1) (2009), 57–64.

 

153. Zoltan Finta and Vijay Gupta, Approximation by q Durrmeyer operators, J Applied Math and Computing 29 (1-2) (2009), 401-415.

 

154. Vijay Gupta and Zoltan Finta, On certain q Durrmeyer operators, Applied Mathematics and Computation 209 (2009), 415-420. ISSN 0096-3003 IF 1.551

 

155. Harun Karsli, Vijay Gupta and A. Izgi, Rate of pointwise convergence of a new kind of Gamma operators for functions of bounded variation, Applied Math Letters 22 (2009), 505-510.

 

156.Vijay Gupta, Approximation for modified Baskakov Durrmeyer type operators, Rocky Mountain J Math 39 (3) (2009), 825-841. 

 

157. Ali Aral and Vijay Gupta, On q-Baskakov type operators, Demonstratio Mathematica  42 (1)  (2009), 109-122.

 

158. Vijay Gupta and A. J. Lopez-Moreno and Jose-Manuel Latorre-Palacios, On Simultaneous Approximation of the Bernstein Durrmeyer Operators, Applied Mathematics and Computation 213 (1) (2009), 112-120. 

 

159. Vijay Gupta, P. N. Agrawal and A R Gairola, On the integrated Baskakov type operators, Applied Mathematics and Computation 213 (2) (2009), 419-425. 

 

160. Sorin Gal and Vijay Gupta, Approximation of vector-valued functions by $q$-Durrmeyer operators with applications to random and fuzzy approximation, Oradea Math. J. 16  (2009), 233-242. 

 

161. N. K. Govil and Vijay Gupta,  Convergence of q-Meyer-Konig-Zeller-Durrmeyer operators, Advanced Studies in Contemporary Mathematics 19 (2009), 97-108.

 

162. X.  M.   Zeng and Vijay Gupta, Approximation by integrated MKZ-Bezier operators in the case , Central European J. Math. 7(3) (2009),  550-557.

 

163. Vijay Gupta and Cristina Radu, Statistical approximation properties of q Baskakov Kantorovich operators, Central Europeon J. Math. 7 (4) (2009), 809-818.

 

164. T. A. K. Sinha, Vijay Gupta, P. N. Agrawal and A. R. Gairola, Inverse theorem for an iterative combinations of Bernstein Durrmeyer operators, Studia Univ. Babes Bolyai Mathematica LIV (4) (2009), 153-164. 

 

165. Vijay Gupta and Ali Aral, Generalized Baskakov Beta operators, Rocky Mountain J. Math. 39 (6) (2009),  1-13.

 

166. P. Maheshwari and V Gupta, On the rate of approximation by modified Beta operators, Int. J. Math Math Sci. Volume 2009 (2009), Article ID 205649, 8 pages

 

167. Vijay Gupta, Certain family of Durrmeyer type operators, Annales Universitatis Mariae Curie-Sklodowska Lublin-Polonia, Series A. Vol. LXIII (2009), 109-115.

 

168.  A. Aral and Vijay Gupta, On the Durrmeyer type modification of the q Baskakov type operators, Nonlinear Analysis: Theory Methods and Applications Volume 72, Issues 3-4, 1 February 2010,  1171-1180.

 

169. Z. Finta and Vijay Gupta Approximation Properties of q Baskakov operators, Central Europeon Journal of Mathematics 8 (1) (2010), 199-211. 

 

170. Vijay Gupta and Ali Aral, Convergence of the q analogue of Szasz Beta operators,  Applied Mathematics and Computation 216 (2010), 374-380.

 

171. Vijay Gupta and X. M. Zeng, Approximation by Bezier variant of the Szasz-Kantorovich Operator in case , Georgian Math J. 17 (2010), 253-260.  

 

172. Vijay Gupta and Honey Sharma, Statistical approximation by q integrated Meyer Konig Zeller Kantorovich operators, Creative Math and Information Theory 19 (1)(2010), 45-52.

 

173.  Vijay Gupta,  On certain type Durrmeyer type q Baskakov operators,  ANNALI DELL'UNIVERSITA' DI FERRARA Volume 56, Issue 2 (2010), 295-303. 

 

174. V Gupta, T. Kim, J. Choi and Y-Hee Kim, Generating functions for q Bernstein, q-Meyer-Konig-Zeller and q-Beta basis, Automation, Computer, Mathematics 19(1) (2010), 7-11.

 

175. Vijay Gupta, A note on q Baskakov-Szasz operators, Lobachevskii Journal of Mathematics 31(4) (2010), 359-366.

 

176. Vijay Gupta and Oktay Duman,  Bernstein Durrmeyer type operators preserving linear functions, Math. Vesniki   62(4) (2010), 259-264.

 

177. Vijay Gupta, A note on modified Phillips operators, Southeast Asian Bulletin of Mathematics 34 (2010), 847-851.

 

178.  Vijay Gupta and N I Mahmudov, Approximation properties of the $q$-Szasz-Mirakjan-Beta operators,  Indian J Industrial and Appl Math 3(2) (2012),  41-53 

 

179. Vijay Gupta and N. Deo, A Note on rate of approximation for certain Bezier-Durrmeyer operators,  Math. Vesniki 63(1) (2011), 27-32.

 

180. Vijay Gupta and T. Kim, On the rate of convergence for q modified Beta operators, Journal of Math. Anal. Appl. 377 (2011), 471-480.  ISSN 0022-247X IF 1.204

 

181. Ali Aral and Vijay Gupta, Generalized Szasz Durrmeyer operators,  Lobachevskii Journal of Mathematics 32 (1) (2011), 23-31.

 

182. Vijay Gupta and Honey Sharma, Recurrence formula and better approximation for q Durrmeyer operators, Lobachevskii Journal of Mathematics 32 (2), (2011), 140-145.

 

183. G. Nowak and Vijay Gupta, The rate of point wise approximation of positive linear operators based on q integers, Ukrianian J. Math.  63 (3) (2011), 350-360.

 

184. Vijay Gupta, P. N. Agrawal and D. K. Verma,  q-Analogue of discrete Beta operators, Annali Dell Universita di Ferrara Volume 57, Issue 1 (2011), 39-66. 

 

185. Ali Aral and Vijay Gupta, Generalized q Baskakov operators, Mathematica Slovaca  61(4) (2011), 619-634. ISSN 0139-991 IF 0.409

 

186. Tuncer Acar, Vijay Gupta and Ali Aral, Rate of convergence for generalized Szasz operators, Bulletin of Math Sci. 1 (2011), 99-113.

 

187. V. Gupta, T. Kim, V. K. Singh and B. Lee, Rate of simultaneous approximation for Baskakov-Szasz operators, Proceedings of the Jangjeon Mathematical Society, 14 (2011), No. 3. pp. 267-275.

 

188. Vijay Gupta and N Deo, A note on improved estimates for integrated Szasz-Mirakyan operators, Mathematica Slovaca 61 (5) (2011), 799-806. 

 

189. Vijay Gupta, Approximation for summation-integral type Beta-Szasz operators, Lobachevskii Journal of Mathematics  32 (3) (2011), 224-230. 

 

190. Vijay Gupta and A. Aral, Approximation by q Baskakov Beta operators, Acta Mathematicae Applicatae Sinica, English Series 27(4) (2011), 569-580.

 

191. Nazim Mamudov  and Vijay Gupta, On certain q analogue of Szasz Kantorovich operators, J. Applied Mathematics and Computing 37 (1-2) (2011), 407-419.

 

192. Sorin G. Gal and Vijay Gupta, Quantative estimates for a new complex Durrmeyer operator in compact disks, Applied Mathematics and Computation 218(6) (2011), 2944-2951. 

 

193. Sorin G. Gal and Vijay Gupta, Approximation by a Durrmeyer-type operator in compact disk, Annali Dell Universita di Ferrara 57 (2011), 261-274.

 

194. Vijay Gupta and Ali Aral, Some approximation properties of q Baskakov Durrmeyer operators,  Applied Mathematics and Computation 218 (3) (2011), 783-788. 

 

195. Vijay Gupta and Rani Yadav, Better approximation by Stancu Beta operators, Rev. D’Anal. Numer Theor L’Approx.  40 (2) (2011), 149-155.

 

196. Ali Aral and Vijay Gupta, On q analogue of Stancu Beta operators, Applied Mathematics Letters 25 (2012), 67-71.

 

197. Vijay Gupta and R. Yadav,  Rate of convergence for generalized Baskakov operators, Arab J. Mathematical Sciences 18 (1) (2012), 39-50.

 

198.  N. I. Mahmudov and Vijay Gupta,  Approximation by Genuine Durrmeyer-Stancu Polynomials in Compact Disks, Mathematical and Computer Modelling 55 (2012), 278-285.

 

199.  D. K. Verma, V. Gupta and P. N. Agrawal, Some approximation properties of Baskakov-Durrmeyer-Stancu operators, Applied Math Computation, 218 (2012), 6549-6556. ISSN 0096-3003 IF 1.551

200. Vijay Gupta and H Karsli, Some approximation properties by q-Sza?sz-Mirakyan-Baskakov-Stancu operators,   Lobachevsky Journal of Math. 33 (2) (2012), 175-182.

 

201. N. K. Govil and Vijay Gupta, q-Beta-Szasz- Stancu Operators, Advanced Studies in Contemperory Mathematics 22(1) (2012), 117-123.

 

202. Sorin G. Gal and Vijay Gupta, Approximation be certain integrated Bernstein type operators in compact disks,  Lobachevskii Journal of Mathematics 33(1) (2012), 39-46.

 

203. S. Gal, Vijay Gupta and N. I. Mahmudov, Approximation by a complex q Durrmeyer type operators, Ann. Univ. Ferrara 58 (1) (2012), 65-87.

 

204. Vijay Gupta and Rani Yadav, Direct estimates in simultaneous approximation for BBS operators, Applied Mathematics and Computation 218 (22) (2012), 11290-11296. 

 

205. N. K. Govil and Vijay Gupta, Rate of approximation for   Szasz-Mirakyan-Stancu-Durrmeyer operators, Lobachevsky Journal of Math 33(3) (2012), 249-254.

 

206. Vijay Gupta, A. Aral and Muzeyyen Ozhavzali, Approximation by q-Szász-Mirakyan-Baskakov operators,  Fasciculi Math. 48 (2012), 35-48.

 

207. R. P. Agarwal and Vijay Gupta, On q-analogue of a complex summation-integral type operators in compact disks, Journal of Inequalities and Applications 2012, 2012:111.

 

208.  S. Gal, Vijay Gupta, D. K. Verma and P. N. Agrawal, Approximation by complex Baskakov-Stancu operators in compact disks, Rend. Circ. Mat. Palermo 61 (2012), 153-165. 

 

209.  Vijay Gupta and D. K. Verma, Approximation by complex Favard-Szasz-Mirakjan-tancu operators in compact disks, Mathematical Sciences 2012, 6:25 

 

210. Vijay Gupta, T. Kim and Sang-Hun Lee, q-analogue of a new sequence of linear positive operators, J. Inequal. Appl. 2012, 2012:144 doi:10.1186/1029-242X-2012-144

 

211. Vijay Gupta, Honey Sharma, Taekyun Kim and Sang-Hun Lee, Properties of q analogue of Beta operators, Advances in Diff Equation 2012, 2012:86 doi:10.1186/1687-1847-2012-86

212. N. Mahmoodov, Vijay Gupta  and H. Kaffaoglu, On certain q-Phillips operators, Rocky Mountain J. Math  42 (4) (2012), 1291-1312.

 

213. Vijay Gupta, D. K. Verma and P. N. Agrawal, Simultaneous approximation by Certain Baskakov-Durrmeyer-Stancu Operators, J. Egyptian Math Soc. 20 (3) (2012), 183-187.

214. Vijay Gupta and R. Yadav, Some approximation results on q-Beta-Szasz operators, Southeast Asian Bulletin of Mathematics 36 (3) (2012), 343-352.

 

215. Sorin G. Gal and Vijay Gupta, Approximation by complex Beta operators of first kind in strips of compact disks, Med J. Math. 10 (1)  (2013),   31-39 

216. Vijay Gupta, Approximation properties by Bernstein-Durrmeyer type operators, Complex Analysis and Operator Theory 7(2013), 363-374. 

 

217. P. N. Agrawal, Vijay Gupta and Satish Kumar, On q-analogue of Bernstein-Schurer-Stancu operators, Applied  Mathematics and Computation 219 (14) (2013), 7754-7764. 

 

218. Ali Aral and Vijay Gupta, On certain Baskakov Durrmeyer operators, Creative Math. Inform. 22(1) (2013), 1-8. 

 

219. H. Karsli and V. Gupta, On convergence of q Chlodovsky type MKZD operators, Math. Vesnik, 65 (2) (2013), 187-196.

 

220. Vijay Gupta, Naokant Deo and X M Zeng, Simultaneous Approximation for Szasz-Mirakian-Stancu-Durrmeyer Operators, Analysis in Theory and Appl. 29(1) (2013), 1-11.

 

221.Vijay Gupta, A New Class of Durrmeyer operators, Advanced Studies in Contemperory Math.  23 (2) (2013), 219-224.

 

222. V. Gupta, P. N. Agrawal and D. K. Verma, A q-Analogue of modified Beta operators, Rocky Mountain J Math. 43( 3)  (2013), 931-947.

 

223. Vijay Gupta and T. Kim, On the q analogue of Baskakov basis function, Russian J. Math. Physics 20 (3) (2013), 191-200. (Springer)

 

224. S. G. Gal and Vijay Gupta, Approximation by Complex Stancu Beta integral operators of second kind in semidisks, Rev. Anal. Numer. Theeor. Approx. 42 (1) (2013), 21-36.

 

225. Vijay Gupta, R. P. Agarwal and D. K. Verma, Approximation for a new sequence of summation-integral type operators, Advances in Mathematical Sciences and Applications 23 (1) (2013), 35-42.

 

226. Vijay Gupta, Combinations of integral operators, Appl. Math. Comput. 224 (2013), 876-881. 

 

227. N. K. Govil, Vijay Gupta and D Soyabos, Certain New classes of Durrmeyer Type operators, Appl. Math. Comput. 225 (2013), 195-203.

 

228.Vijay Gupta, Convergence of Szasz Beta operators, Ann. Univ. Ferrara 59 (2013), 311-318.

 

229. Vijay Gupta and Rani Yadav, Approximation by complex summation-integral type operators in compact disks, Mathematica  Slovaca 63 (5) (2013), 1025-1036.

 

230. X. M. Zeng, Vijay Gupta and O. Agratini, Rate of approximation by Bezier variant of the Baskakov-Kantorovich operators in case , Rocky Mountain J Math.  44 (1) (2014), 317-327.

 

231. Vijay Gupta and H. Karsli, Approximation for certain Durrmeyer-Stancu operators in compact disks, Southeast Asian Bulletin of Math. 38(3) (2014), 359-368.

 

232. Vijay Gupta, G. Tachev, Approximation by Szasz-Mirakyan Baskakov operators, J. Appl. Funct. Anal. 9 (3-4) (2014), 308-319. 

 

233. Vijay Gupta, Stancu variant of Beta-Szasz operators, Georgian Math. J. 21 (1) (2014), 75-82.

 

234. Vijay Gupta and Themistocles M. Rassias, Lupas durmeyer operators based on Polya distribution, Banach J Math Anal. 8 (2) (2014), 146-155.

 

235. S. G. Gal, Vijay Gupta, Approximation by complex Szasz-Durrmeyer operators in compact disks, Acta Math. Sci. 34 B (4) (2014), 1157-1165.

 

236. S. G. Gal and Vijay Gupta, Approximation by complex Phillips-Stancu operators in compact disks under exponential growth, Applied Math. Comput. 234 (2014), 309-315. 

 

237. Vijay Gupta, Th. M. Rassias and Rani Yadav, Approximation by Lupas Beta integral operators, Applied Math. and Computation 236 (1) (2014), 19-26. 

 

238. P. N. Agrawal, Vijay Gupta, A Sathish Kumar, A. Kajla, Generalized Baskakov Szasz type operators,  Appl. Math. Comput. 236 (1) (2014), 311-324. 

 

239. N. I. Mahmudov and Vijay Gupta, Approximation by complex q-Durrmeyer polynomials in compact disks, Acta Math Appl. Sinica 30 (1) (2014), 65-74.

 

240. Vijay Gupta, Complex Baskakov-Szasz operators in compact semi-disks, Lobachevskii J. Math. 35 (2) (2014), 65-73.

 

241.Vijay Gupta and Rani Yadav, On the approximation of certain integral operators, Acta Math Vietnamica 39 (2014), 193-203.

 

242. P. N. Agrawal, Vijay Gupta and A. Sathish Kumar, Generalized Baskakov-Durrmeyer type operators, Rend. Conti del Circolo Matematico di Palermo 63(2) (2014), 193-209.

 

243. Vijay Gupta and Danyal Sobayus, Approximation by complex genuine hybrid operators, Appl. Math. Computation 244 (2014), 526-532. 

 

244. Daniel Cardenas-Morales and Vijay Gupta, Two families of Bernstein-Durrmeyer type operators, Appl. Math. Computation  248 (2014), 342-353. 

 

245. Vijay Gupta and Gancho Tachev, Approximation by linear combinations of complex Phillips operators in compact disks, Results in Math. 66 (2014), 265-272. IF 0.864

 

246. Vijay Gupta and Th M Rassias, Direct Estimates for Certain Sz\'asz type operators, Applied Mathematics and Computation 251(2015), 469-474. IF 1.551

 

247. Vijay Gupta, Direct estimates for a new general family of Durrmeyer type operators, Bollettino dell'Unione Matematica Italiana 7 (2015), 279-288.

 

248. Vijay Gupta and N. Malik, Approximation for genuine summation-integral type operators, Appl. Math. Comput. 260 (2015), 321-330. 

 

249. S. G. Gal, Vijay Gupta, Approximation by complex Szasz-Mirakyan-Stancu-Durrmeyer operators   in compact disks under Exponential Growth, Filomat 29(5) (2015), 1127-1136.

 

250. S G Gal and Vijay Gupta, Complex form of a link operator between the Phillips and the Szasz-Mirakjan operators, Results in Math 67 (3-4) (2015), 381-393. 

 

251. Vijay Gupta, Overconvergence of Complex Baskakov–Szász–Stancu Operators, Mediterranean Journal of Mathematics 12 (2) (2015), 455-470. 

 

252. T. Acar, A. Aral and Vijay Gupta, On approximation properties of a new type Bernstein-Durrmeyer operators, Mathematica Slovaca 65 (5) (2015), 1107-1122. 

 

253. S. G. Gal and Vijay Gupta, Approximation by complex Baskakov-Szasz-Durrmeyer operators in compact disks, Analysis in Theory and Applications 31 (2) (2015), 207-220.

 

254. Vijay Gupta and G. C. Greubel, Moment estimations of a new Szasz-Mirakyan-Durrmeyer operators, Appl. Math Comput.  271 (2015), 540-547. IF 1.551

 

255.  U. Abel, Vijay Gupta and Mircea Ivan, A generalization of a combinatorial identity by Chang and Xu, Bull. Math Sci. 5 (3) (2015), 511-516. 

 

256.Vijay  Gupta and G. Tachev, Upper estimates for general complex Baskakov Szasz operators, J. Classical Analysis 7(1) (2015), 17-23.

 

257. Meenu Goyal, Vijay Gupta and P. N. Agrawal, Quantative convergence results for a family of hybrid operators, Appl Math Comput 271 (2015),  893-904.

 

258. D. K. Verma and Vijay Gupta, Approximation for Jakimovski-Leviatan-Paltanea operators, Annali dell'Università di Ferrara 61(2) (2015), 367-380.

 

259. S. G. Gal and Vijay Gupta, Approximation by complex Lupas-Durrmeyer polynomials based on Polya distribution, Banach J. Math Anal. 10 (1) (2016), 209-221.

 

260. Vijay Gupta, Th M Rassias, Honey Sharma, q Durrmeyer operators based on Polya distribution, J. Nonlinear Sci. Appl. 9 (2016), 1497-1504.

 

261. Vijay Gupta and A. Aral, Bernstein Durrmeyer operators based on two parameters, Facta Universitatis, Series: Mathematics and Informatics 31(1) (2016), 79-95.

 

262. O. Agratini and Vijay Gupta, On the uniform convergence of q series, Carpathian J Math. 32 (2) (2016).

 

263. Ali Aral and Vijay Gupta, Direct estimates for Lupas Durrmeyer operators, Filomat 30 (1) (2016), 191-199. 

 

264. Vijay Gupta and Neha Malik, Direct estimations of new generalized Baskakov-Szasz operators, Publ. Math. Inst. (Beograd) 99 (113) (2016), 265-279.

 

265.Vijay   Gupta and G. Tachev, General form of Voronovskaja's theorem in terms of weighted modulus of continuity,  Results Math 69  (3-4) (2016), 419-430.

 

266. Vijay Gupta, (p,q)-Baskakov-Kantorovich operators, Appl. Math. Inf. Sci., 10 (4) (2016), 1551-1556.

 

267. Vijay Gupta, (p,q) Genuine Bernstein Durrmeyer operators, Bull Un Matt. Ital. 9(3) (2016), 399-409.

 

268. A. Aral, E. Deniz and Vijay Gupta, On Modification of the Szasz-Durrmeyer Operators, Georgian Math. J. 23 (3) (2016), 323-328.

 

269. Vijay Gupta and Danyal Soybas, Convergence of integral operators based on different distributions, Filomat 30 (8) (2016), 2277-2287.

 

270. A. Aral and Vijay Gupta, (p,q)-Type Beta functions of second kind, Advances in Operator Theory 1(1) (2016), 134-144.

 

271. Vijay Gupta, Th. M.  Rassias, (p,q)-Genuine Baskakov-Durrmeyer operators, International Journal of Nonlinear Analysis and Applications 7(2) (2016), 69-76.

 

272. N. Malik and Vijay Gupta, Approximation by (p,q) Baskakov Beta operators, Applied Math. Computation 293 (2017), 49-56.

 

273. Vijay Gupta, Ana Maria Acu and Daniel Florin Sofonea, Approximation of Baskakov type Polya Durrmeyer operators, Appl. Math. Comput. 294 (2017), 318-331. 

 

274. Vijay Gupta and N. Malik, Approximation of functions by complex genuine Polya-Durrmeyer operators, Computational Methods and Function Theory 17(1) (2017), 3-17.

 

275. Vijay Gupta, T M Rassias and E Pandey, On Genuine Lupa¸s-Beta operators and Modulus of Continuity  Int J. Nonlinear Anal Appl. 8 (1) (2017), 23-32.

 

276. Zoltan Finta and Vijay Gupta Approximation theorems for limit (p,q)-Bernstein-Durrmeyer operators, Facta Univ. (NIS) 32 (2) (2017), 195-207.

 

277. A. Aral and Vijay Gupta, (p,q)-Variant of Szász-Beta operators, Revista de la Real Academia de Ciencias Exactas, Físicas y. 111 (2017), 719-733.

 

278. Vijay Gupta and Neha Malik, Approximation with certain Szasz-Mirakyan operators, Khayyam J. Math. 3(2) (2017), 90-97.

 

279. Ali Aral and Vijay Gupta, Applications of (p,q)-Gamma Function to Szasz Durrmeyer operators, Publ Inst Math. Belgrade 102(116) (2017), 211–220.

 

280. Vijay Gupta and Gancho Tachev,  Approximation by Phillips operators preserving exponential functions, Medett. J. Math. 14 (2017), Art. 177.

 

281. Ana Maria Acu and Vijay Gupta, Direct results for certain summation-integral type Baskakov-Sz\'{a}sz operators, Results Math. 72(3) (2017), 1161-1180.

 

282. Ovgu  Gurel Yi lmaz, Vijay Gupta and Ali Aral, On Baskakov Operators preserving exponential function, J. Numer. Anal. Approx. Theory 46(2) (2017), 150-161. 

 

283. Vijay Gupta and Deepika Agrawal, Approximation results by certain genuine operators of integral type, Kragujevac Journal of Mathematics 42(3) (2018), 335-348.

 

284. Emre Deniz, Ali Aral and Vijay Gupta, Note on Sz\'asz-Mirakyan-Durrmeyer operators preserving $e^{2ax},a>0$, Numerical Functional Analysis and Optimization 39(2)(2018), 201-207.

 

285. Vijay Gupta, (p,q)-Szasz-Mirakyan-Baskakov operators, Complex Analysis and Operator Theory 12(1) (2018), 17-25.

 

286. Vijay Gupta and N. Malik, Genuine link Baskakov Durrmeyer operators, Georgian Math J. 25(1) (2018), 25-40.

 

287. G. V. Milonovic, Vijay Gupta and N. Malik, (p,q)-Beta functions and applications in approximation, Boletín de la Sociedad Matemática Mexicana, Tercera Serie 24 (1) (2018), 219-237

 

288.Vijay Gupta and Ali Aral, A note on Szasz-Mirakyan-Kantorovich type operators preserving $e^{-x}$, Positivity 22 (2) (2018), 415-423.

 

289. Vijay Gupta and Ana Maria Acu, On Baskakov-Szasz-Mirakyan type operators preserving exponential functions, Positivity 22(3) (2018), 919–929.

 

 

 

290. Vijay Gupta and H. M. Srivastava, A general family of the Srivastava-Gupta operators preserving linear functions, European J. Pure Appl. Math. 11(3) (2018), 575-579.

 

291. Vijay Gupta,  Differences of operators of Lupas type, Constructive Mathematical Analysis 1(1) (2018), 9-14.

 

292. Ana Maria Acu, Vijay Gupta and N. Malik, Local and global approximation for certain (p,q)-Durrmeyer type operators, Complex Analysis and Operator Theory 12 (8) (2018), 1973-1989.

 

293. S G Gal and Vijay Gupta, Approximation by a Complex Post-Widder Type Operator, Analysis in Theory and Applications 34(4) (2018), 297-305.

 

294. Vijay Gupta, Some Examples of Genuine Approximation Operators, General Mathematics 26(1) (2018).

 

295. Vijay Gupta, Th. M. Rassias, P. N. Agrawal and Meenu Goyal, Approximation with Certain Genuine Hybrid Operators, Filomat 32 (6) (2018),  2335-2348.

 

296. Vijay Gupta and Antonio-Jesús López-Moreno, Phillips operators preserving arbitrary exponential functions, $e^{at}$, $e^{bt}$, Filomat 32 (14) (2018). 

 

297. Vijay Gupta and Gancho Tachev, A note on the differences of two positive linear operators, Constructive Mathematical Analysis 2(1) (2019), 1-7.

 

298. Vijay Gupta and Deepika Agrawal, Convergence by modified Post-Widder operators, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 113(2)(2019),  1475-1486.

 

299. Vijay Gupta, Prerna Maheshwari, Approximation with certain Post-Widder operators, Publ Inst Math, 105(119) (2019), 1-6.

 

300. Vijay Gupta, Ana Maria Acu and Gancho Tachev, Modified Kantorovich operators with better approximation properties, Numerical Algorithm. 81(1)(2019), 125-149. 

 

301. Vijay Gupta, General estimates for the difference of operators, Computational and Mathematical Methods 1(2) (2019) e1018 

 

302. Deepika Agrawal and Vijay Gupta, Generalized Hybrid Operators Preserving Exponential Functions, Asian-European J. Math. 12 (1) (2019), 1950085 (11 pages).

 

303. A M Acu, Vijay Gupta, G. Tachev,  Better numerical approximation by Durrmeyer type operators, Results Math. 74 (90) (2019).

 

304. Vijay Gupta, On difference of operators with applications to Sz\'asz type operators, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 113 (3) (2019), 2059-2071 

 

305. Vijay Gupta, Danyal Soybas and Gancho Tachev, Improved approximation on Durrmeyer type operators, Boletín  de la Sociedad Matemática Mexicana 25(2) (2019), 363-373.

 

306. Vijay Gupta, A note on general family of operators preserving linear functions, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 113 (4) (2019), 3717-3725 

 

307. Vijay Gupta and Ana Maria Acu, On difference of operators with different basis functions, Filomat 33 (10) (2019), 3023-3034.

 

308. Vijay Gupta, Differences of operators of Baskakov type, Fasciculi Math. 62 (2019), 47-55.

 

309. Vijay Gupta, D Agarwal and T M Rassias, Quantitative Estimates for Differences of Baskakov-type Operators, Complex Anal. Oper. Theory 13(8) (2019), 4045-4064. 

 

310. O. G. Yilmaz, Vijay Gupta and Ali Aral,  A note on Baskakov-Kantorovich type operators preserving e^{-x}, Math. Meth. Appl. Sci https://doi.org/10.1002/mma.5337.

 

311. Vijay Gupta, Approximation with certain exponential operators, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 114 (2) (2020), Art 51.

 

312.Vijay Gupta, A large family of linear positive operators,  Rend. Circ. Mat. Palermo, II. Ser (2019). https://doi.org/10.1007/s12215-019-00430-3  

 

313. Vijay Gupta, Convergence estimates for Gamma operator, Bull Malaysian Math Soc. June 2019,  https://doi.org/10.1007/s40840-019-00791-z

 

314. Vijay Gupta, Estimate for the difference of operators having different basis functions, RCMP, Rendiconti del Circolo Matematico di Palermo Series 2 https://doi.org/10.1007/s12215-019-00451-y

 

(ii) Books

 

Ali Aral, Vijay Gupta and Ravi P. Agarwal, Applications of q Calculus in Operator Theory, Springer 2013, XII, 262 p.  ISBN 978-1-4614-6945-2

Vijay Gupta and Ravi P. Agarwal, Convergence Estimates in Approximation Theory, Springer 2014, ISBN 978-3-319-02765-4

Vijay Gupta and Gancho Tachev, Approximation with Positive Linear Operators and Linear Combinations, Series: Developments in Mathematics, Springer. Cham. 2017.

Vijay Gupta, Th. M. Rassias, P. N. Agrawal and Ana Maria Acu, Recent Advances in Constructive Approximation Theory, Series: Springer Optimization and Its Applications, Springer, Cham.  2018. DOI 10.1007/978-3-319-92165-5.

Vijay Gupta and M. T. Rassias, Moments of Linear Positive Operators and Approximation, Series: SpringerBriefs in Mathematics, Springer Nature Switzerland AG (2019). 

 

 

(iii) Edited Books

 

T.M. Rassias, Vijay Gupta (Eds.) Mathematical Analysis, Approximation Theory and Their Applications Series: Springer Optimization and Its Applications, Vol. 111 (2016) ISBN 978-3-319-31279-8.

V. K. Singh, H.M. Srivastava, E.Venturino, M. Resch, Vijay Gupta, (Eds.), Modern Mathematical Methods and High Performance Computing in Science and Technology M3HPCST, Ghaziabad, India, December 2015, Springer Proceedings in Mathematics & Statistics, (2016).

Naokant Deo, Vijay Gupta, Ana Maria Acu and P. N. Agrawal, Mathematical Analysis I – Approximation Theory ICRAPAM 2018, New Delhi, India, October 23–25 Series: Springer Proceedings in Mathematics & Statistics, Vol. 306 (2019)

Naokant Deo, Vijay Gupta, Ana Maria Acu and P. N. Agrawal, Mathematical Analysis II – Optimisation, Differential Equations and Graph Theory ICRAPAM 2018, New Delhi, India, October 23–25 Series: Springer Proceedings in Mathematics & Statistics, Vol. 307 (2019)

 

 

(iv) Open Problems

 

Vijay Gupta, Recurrence relation for moments, Newsletter, European Math Soc. 91 (2014) pp 64. Prob 130

Vijay Gupta, Identity for rising factorial, Newsletter, European Math. Soc. 91 (2014) pp 64.Prob 129.

Vijay Gupta, Solved and unsolved problems, European Math. Soc. Newsletter 95 (March, 2015), pp. 61, Prob. 139.

Vijay Gupta, Solved and unsolved problems, European Math. Soc. Newsletter 95 (March, 2015), pp. 61, Prob. 140.

Vijay Gupta, Solved and unsolved problems, European Math. Soc. Newsletter 97 (Sept, 2015), pp. 68, Prob. 153.

Vijay Gupta, Solved and unsolved problems, European Math. Soc. Newsletter 97 (Sept, 2015), pp. 68, Prob. 154.

 

 (v)    Book   Chapters

 

N. K. Govil and Vijay Gupta, Some approximation properties of integrated Bernstein operators, Advances in Mathematics Research, Vol. 11, 2009 Chapter 8. Nova Science Publishers, Inc. Editor: Albert R. Baswell [R] ISBN 978-1-60876-970-4.  

Vijay Gupta and T. Shervashidze, Upper bound for Bernstein basis function, Prokhorov and Contemperory Probability Theory, In Honor of Yuri V. Prokhorov, Series: Springer Proceedings in Mathematics & Statistics, Vol. 33 Shiryaev, Albert N.; Varadhan, S. R. S.; Presman, Ernst L. (Eds.) 2013, XXXVIII, 446 p. Chapter 17.

N. K. Govil and Vijay Gupta, Simultaneous Approximation for Stancu Type Generalization of Certain Summation-Integral Type Operators, Analytic Number Theory, Approximation Theory and Special Functions, Eds. K. Alladi, G.V. Milovanovic and Michael Th. Rassias, Springer-Verlag 2014. 

N. K. Govil and Vijay Gupta, Approximation properties of Phillips operators, Mathematics without Boundries: Surveys in Pure Mathematics, Eds.: Th. M. Rassias and Panos Pardalos,  Springer-Verlag 2014, p.p. 221-243.

Sorin G. Gal and Vijay Gupta Approximation by complex Durrmeyer type operators in compact disks, Mathematics without Boundaries; Surveys in Interdisciplinary Research ed. P. Pardalos and T. M. Rassias Springer 2014, pp 263-285.

Vijay Gupta, Different Durrmeyer Variants of Baskakov Operators, Topics in Mathematical Analysis and Applications, Springer Optimization and Its Applications 94, T. Rassias and L. Tóth (eds.), © Springer International Publishing Switzerland 2014. DOI 10.1007/978-3-319-06554-0__17

 N. K. Govil, Vijay Gupta and Danyal Soybas, Certain Szasz-Mirakyan Beta operators, Topics in Mathematical Analysis and Applications, Springer Optimization and Its Applications 94, T. Rassias and L. Tóth (eds.), © Springer International Publishing Switzerland 2014. 

 

Vijay Gupta, Themistocles M. Rassias, Hypergeometric Representation of

Certain Summation-Integral Operators, Topics in Mathematical Analysis and Applications, Springer Optimization and Its Applications 94, T. Rassias and L. Tóth (eds.), © Springer International Publishing Switzerland 2014. DOI 10.1007/978-3-319-06554-0_18

Vijay Gupta, On Approximation Properties of Szasz-Mirakyan Operators, Handbook on Functional Inequalities Series: Springer Optimization and Its Applications, Vol. 95, Rassias, Themistocles M. (Ed.) Springer-Verlag 2014.

Vijay Gupta, Approximation By Durrmeyer Type Operators Preserving Linear Functions, Computation, Cryptography and Network Security, Springer 2015 ed. Michael Th. Rassias and N. Daras, pp 289-298.

Vijay Gupta, Th. M.   Rassias and J. Sinha, A survey on Durrmeyer operators, Springer International Publishing Switzerland (2016), 299-312,  P.M. Pardalos, Th. M. Rassias (eds.), Contributions in Mathematics and Engineering, DOI 10.1007/978-3-319-31317-7_14 

Vijay Gupta, Approximation by generalization of Baskakov-Durrmeyer operators, Mathematical Analysis, Approximation Theory and their Applications Series: Springer Optimization and Its Applications, Vol. 111 (2016) Ed. Th M Rassias and V. Gupta.

Vijay Gupta and Deepika Agrawal,  Approximation by Lupas-Kantorovich operators, Modern Discrete Mathematics and Analysis, Springer 2017  Edited by N. J. Daras  and Th. M. Rassias

Vijay Gupta, Neha Malik and Th. M. Rassias, Moment Generating Functions and Moments of linear positive operators, Modern Discrete Mathematics and Analysis, Springer 2017  Edited by N. J. Daras  and Th. M. Rassias

Vijay Gupta, Approximation by generalizations of hybrid Baskakov type operators preserving exponential functions, Mathematical Analysis and Applications: Selected Topics, Wiley, Eds. Michael Ruzhansky, Hemen Dutta, Ravi P. Agarwal, April 2018 ISBN: 978-1-119-41434-6

  

(vi) Full PAPERS PUBLISHED IN PROCEEDINGS

 

1.  M. Saleem, S. U. Siddiqui and Vijay Gupta, Young predation and time delays, Mathematical Modeling of Environmental and Ecological Systems, Elsevier Science Publishers B.V. (1987), 179-192.

 

2. Vijay Gupta and Ashok Sahai, Rate of convergence for Phillips operators of function of bounded variation, Proc. First Annual Conf. of Industrial and Applied Math., Roorkee 1993.

 

3. Vijay Gupta, Global simultaneous approximation by modified Beta operators, Proc of the 26th Annual Conf. Kerman, Iran (1995), 421-424.

 

4. G. S. Srivastava Vijay Gupta and A. Sahai, Saturation theorem for linear combinations of Phillips operators, Approx. Theory and its Appl., New Age International Ltd, Publ.  (1996), 59-67.

 

5.   A. Sahai and Vijay Gupta, Rate of convergence by Szasz Beta operators, Approx. Theory and its Appl., New Age International Ltd, Publ. (1996), 80-86.