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Approximation by genuine Gupta–Srivastava operators

  • Ram Pratap
  • Naokant DeoEmail author
Original Paper
  • 19 Downloads

Abstract

In the present paper, we consider new operators, which is defined by Gupta and Srivastava (Eur J Pure Appl Math 11(3):575–579, 2018). They considered a general sequence of positive linear operators and gave the modified form of their previous operators (Neer et al. in Math Comput Model 37:1307–1315, 2003). As these operators preserve linear functions, we call these operators as genuine Gupta–Srivastava operators. Here we discuss some basic properties, direct results and rate of convergence of functions of bounded variation and weighted approximation.

Keywords

Baskakov operators Hypergeometric function Function of Bounded variation 

Mathematics Subject Classifications

41A25 42A36 

Notes

Acknowledgements

The authors are thankful to the referee for his valuable comments leading to the overall improvements in the paper.

References

  1. 1.
    Acu, A.M., Gupta, V.: Direct results for certain summation-integral type Baskakov-Szász operators. Results Math. 72(3), 1161–1180 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Acu, A.M., Agrawal, P.N., Neer, T.: Approximation properties of the modified Stancu operators. Numer. Funct. Anal. Optim. 38(3), 279–292 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bustamante, J.: Bernstein Operators and Their Properties. Birkhäuser, Basel (2017)CrossRefzbMATHGoogle Scholar
  4. 4.
    Deo, N.: Faster rate of convergence on Srivastava-Gupta operators. Appl. Math. Comput. 218(21), 10486–10491 (2012)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Deo, N., Dhamija, M.: Generalized positive linear operators based on PED and IPED. Iran J Sci Technol Trans Sci (2018).  https://doi.org/10.1007/s40995-017-0477-5
  6. 6.
    DeVore, R.A., Lorentz, G.G.: Constructive Approximation. Springer, Berlin (1993)CrossRefzbMATHGoogle Scholar
  7. 7.
    Gadjiev, A.D., On, P.P.: Korovkin type theorems. Math. Zametki. 205, 781–786 (1976)Google Scholar
  8. 8.
    Ibikli, E., Gadjieva, E.A.: The order of approximation of some unbounded function by the sequence of positive linear operators. Turkish J. Math. 193, 331–337 (1995)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Gupta, V., Agarwal, R.P.: Convergence Estimates in Approximation Theory. Springer, Heidelberg (2016)zbMATHGoogle Scholar
  10. 10.
    Gupta, V.: An estimate on the convergence of Baskakov–Bézier operators. J. Math. Anal. Appl. 312(1), 280–288 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Gupta, V., Rassias, ThM, Agrawal, P.N., Acu, A.M.: Recent Advances in Constructive Approximation Theory. Springer, Cham (2018)CrossRefzbMATHGoogle Scholar
  12. 12.
    Ispir, N.: On modified Baskakov operators on weighted spaces. Turkish J. Math. 25(3), 355–365 (2001)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Ispir, N., Yüksel, I.: On the Bézier variant of Srivastava-Gupta operators. Appl. Math. Notes 5, 129–137 (2005)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Maheswari(Sharma), P.: On modified Srivastava-Gupta operators. Filomat 29(6), 1173–1177 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Neer, T., Ispir, N., Agrawal, P.N.: Bézier variant of modified Srivastava-Gupta operators. Revista de la Unión Matemat́ica Argentina 58(2), 199–214 (2017)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Srivastava, H.M., Gupta, V.: A Certain family of summation-integral type operators. Math. Comput. Model. 37, 1307–1315 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Gupta, V., Srivastava, H.M.: A general family of the Srivastava-Gupta operators preserving linear functions. Eur. J. Pure Appl. Math. 11(3), 575–579 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Verma, D.K., Agrawal, P.N.: Convergence in simultaneous approximation for Srivastava-Gupta operators. Math. Sci. (2012).  https://doi.org/10.1186/2251-7456-6-22
  19. 19.
    Yadav, R.: Approximation by modified Srivastava-Gupta operators. Appl. Math. Comput. 226, 61–66 (2014)MathSciNetzbMATHGoogle Scholar

Copyright information

© The Royal Academy of Sciences, Madrid 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsFormerly Delhi College of Engineering, Delhi Technological UniversityDelhiIndia

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