Skip to main content
Log in

On Kantorovich Variant Based on Inverse Pólya–Eggenberger Distribution

  • Published:
Bulletin of the Malaysian Mathematical Sciences Society Aims and scope Submit manuscript

Abstract

This article provides a link between the generalized Baskakov operators, and its Kantorovich-type integral variant, using the technique of finite difference. It is pointed out that one has to modify slightly the integral variant to find a connection. We estimate some direct results and difference estimates of the Kantorovich variant with the discrete operators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Acu, A.M., Muraru, C.V.: Certain approximation properties of Srivastava–Gupta operators. J. Math. Inequal. 12(2), 583–595 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  2. Agrawal, P.N., Acu, A.M., Sidharth, M.: Approximation degree of a Kantorovich variant of Stancu operators based on Pólya-Eggenberger distribution. Rev. Real Acad. Cienc. Exact. Fís. Nat. Ser A Mat. RACSAM 113(12), 137–156 (2017). https://doi.org/10.1007/s13398-017-0461-0

    Article  MATH  Google Scholar 

  3. Aral, A., Inoan, D., Rasa, I.: On differences of linear positive operators. Anal. Math. Phys. 9, 1227–1239 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  4. Baxhaku, B., Berisha, A.: Approximation by a sequence of operators of the Srivastava-Gupta type involving the Brenke polynomials with a certain parameter. Math. Methods Appl. Sci. 42(6), 1984–1998 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  5. Deo, N., Dhamija, M., Miclǎuş, D.: Stancu-Kantorovich operators based on inverse Pólya-Eggenberger distribution. Appl. Math. Comput. 273, 281–289 (2016). https://doi.org/10.1016/j.amc.2015.10.008

    Article  MathSciNet  MATH  Google Scholar 

  6. Gupta, V.: Higher order Lupaş-Kantorovich operators and finite differences. Rev. Real Acad. Cienc. Exact. Fís. Nat. Ser A Mat. RACSAM 115, 100 (2021). https://doi.org/10.1007/s13398-021-01034-2

    Article  MathSciNet  MATH  Google Scholar 

  7. Gupta, V.: On difference of operators with applications to Szász type operators. Rev. Real Acad. Cienc. Exact. Fís. Nat. Ser A Mat. RACSAM 113(3), 2059–2071 (2019)

    MATH  Google Scholar 

  8. Gupta, V., Acu, A.M., Sofonea, D.F.: Approximation of Baskakov type Pólya-Durrmeyer operators. Appl. Math. Comput. 294, 318–331 (2017). https://doi.org/10.1016/j.amc.2016.09.012

    Article  MathSciNet  MATH  Google Scholar 

  9. Gupta, V., Agarwal, D., Rassias, T.M.: Quantitative estimates for differences of Baskakov-type operators. Complex Anal. Oper. Theory 13(8), 4045–4064 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ispir, N., Yuksel, I.: On the Bézier variant of Srivastava-Gupta operators. Appl. Math. E-Notes 5, 129–137 (2005)

    MathSciNet  MATH  Google Scholar 

  11. Özarslan, M.A.: Approximation properties of Jain-Appell operators. Appl. Anal. Discret. Math. 14, 654–669 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  12. Srivastava, H.M., Gupta, V.: A certain family of summation integral type operators. Math. Comput. Modelling 37, 1307–1315 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Stancu, D.D.: Approximation of functions by a new class of linear polynomial operators. Rev. Roum. Math. Pures et Appl. 13, 1173–1194 (1968)

    MathSciNet  MATH  Google Scholar 

  14. Stancu, D.D.: Two classes of positive linear operators. Anal. Univ. Timişoara. Ser. Matem. 8, 213–220 (1970)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the reviewer(s) and the handling editor for their helpful suggestions, leading to the overall improvement in the manuscript.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vijay Gupta.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Communicated by Nur Nadiah Abd Hamid.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gupta, V., Anjali On Kantorovich Variant Based on Inverse Pólya–Eggenberger Distribution. Bull. Malays. Math. Sci. Soc. 46, 2 (2023). https://doi.org/10.1007/s40840-022-01398-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40840-022-01398-7

Keywords

Mathematics Subject Classification

Navigation