Skip to main content
SpringerLink
Log in

On Bounded Variation Functions by General MKZD Operators

  • ORIGINAL ARTICLES
  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

In this paper, we study the rate of convergence for functions of bounded variation for the recently introduced Bzier variant of the Meyer–Knig–Zeller–Durrmeyer operators.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Meyer-Knig, W., Zeller, K.: Bernsteinsche Pootenzreihen. Studia Math., 19, 89–94 (1960)

    Google Scholar 

  2. Cheney, E. W., Sharma, A.: Bernstein power series. Canad. J. Math., 16, 241–253 (1964)

    MATH  Google Scholar 

  3. DeVore, R. A.: The approximation of continuous functions by positive linear operators, Lecture Notes in Math. Springer, New York, 1972

  4. Guo, S.: Degree of approximation to functions of bounded variation by certain operators. Approx. Theory and Its Appl., 4(2), 9–18 (1988)

    MATH  Google Scholar 

  5. Gupta, V.: A sharp estimate on the degree of approximation to functions of bounded variation by certain operators. Approx. Theory and Its Appl., 11(3), 106–107 (1995)

    MATH  Google Scholar 

  6. Gupta, V., Ahmad, A.: An improved estimate on the degree of approximation to functions of bounded variation by certain operators. Revista Colombiana de Matematicas, 29, 119–126 (1995)

    MATH  Google Scholar 

  7. Zeng, X. M.: Rates of convergence of bounded variation functions by two generalized Meyer–Knig and Zeller type operators. Comput. Math. Appl., 39, 1–13 (2000)

    Article  MATH  Google Scholar 

  8. Guo, S.: On the rate of convergence of the integrated Meyer–Konig and Zeller operators for functions of bounded variation. J. Approx. Theory, 56, 245–255 (1989)

    Article  MATH  Google Scholar 

  9. Zeng, X. M., Piriou, A.: On the rate of convergence of two Bernstein–Bzier type operators for bounded variation functions. J. Approx. Theory, 95, 369–387 (1998)

    Article  MATH  Google Scholar 

  10. Zeng, X. M., Chen, W.: On the rate of convergence of the generalized Durrmeyer type operators for functions of bounded variation. J. Approx. Theory, 102, 1–12 (2000)

    Article  MATH  Google Scholar 

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

    Google Scholar 

  12. Abel, U., Gupta, V., Ivan, M.: The complete asymptotic expansion for a general Durrmeyer variant of the Meyer–Koing and Zeller operators. Mathematical and Computer Modelling, 40, 867–875 (2004)

    Article  MATH  Google Scholar 

  13. Gupta, V., Abel, U.: The rate of convergence by a new type of Meyer–Konig and Zeller operators. Fasciculi Math., 34, 15–23 (2004)

    MATH  Google Scholar 

  14. Zeng, X. M.: Bounds for Bernstein basis functions and Meyer–Knig and Zeller basis functions. J. Math. Anal. Appl., 219, 364–376 (1998)

    Article  MATH  Google Scholar 

  15. Abel, U., Gupta, V., Ivan, M.: On the rate of convergence of a Durrmeyer variant of the Meyer–Konig and Zeller operators. Archiv. Inequal. Appl., 1, 1–10 (2003)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Applied Sciences, Netaji Subhas Institute of Technology, Azad Hind Fauj Marg, Sector 3 Dwarka, New Delhi-110075, India

    Vijay Gupta*

Authors
  1. Vijay Gupta*
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vijay Gupta*.

Additional information

The research partially supported by Department of Mathematics and Statistics, Auburn University, AL, USA

*Presently the author is on leave from NSIT, India, and working in Department of Mathematics and Statistics, Auburn University, Auburn, AL USA

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gupta*, V. On Bounded Variation Functions by General MKZD Operators. Acta Math Sinica 23, 1457–1462 (2007). https://doi.org/10.1007/s10114-005-0776-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-005-0776-1

Keywords

MR (2000) Subject Classification

Search

Navigation