Skip to main content
SpringerLink
Log in

TheL p-saturation results weighted simultaneous approximation by the method of Bernstein-Durrmeyer operators

  • Published:
Approximation Theory and its Applications

Abstract

The aim of the present paper is to prove new equivalence results and Lp-stauration results on weighted simultaneous approximation by the method of Bernstein-Durrmeyer operators (including results in [7]). One of the main tools and crucial estimates managing the converse results is given by a direct modified Vornorskaja theorem which uses the third order weighted modulus of smoothness.

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. Butzer, P. L. and Nessel, R. J., Fourier Analysis and Approximation, Birkhaser, 1971.

  2. Chen, W., On the Approximation by the Mixed Exponential type Integral Operators Approx. Theory and its Appl. 5(1989), No. 2, 9–23.

    MATH  Google Scholar 

  3. Ditzian, Z. and Totik, “Moduli of Smoothness”, Springer-Verlag, Berlin, New York, 1987.

    MATH  Google Scholar 

  4. Ditzian, Z. and Ivanov, K., Bernstein-Type Operators and Their Derivatives, J. Approx. Theory 56(1989), 72–90.

    Article  MATH  MathSciNet  Google Scholar 

  5. Gonska, H. H. and Zhou, X., A global inverse theorem on simultaneous Approximation by Bernstein-Durrmeyer Operators, J. Approx. Theory 67(1991), 284–304.

    Article  MATH  MathSciNet  Google Scholar 

  6. Hardy, G. H., Inequalities, Cambridge University Press, 2nd Edition 1952.

  7. Heilmann, M. and Muller, M. W., Direct and Converse Results on Weighted Simultaneous Approximation by the Method of Operators of Baskakov-Durrmeyer type. Rusults Math. 16(1989), 228–242.

    MathSciNet  Google Scholar 

  8. Heilmann, M. and Muller, M. W., Equivalence of a Weighted Modulus of Smoothness and a Modified Weighted K-Functional, Progress in Approximation Theory, Academic, Press, New York (1991), 467–473.

    Google Scholar 

  9. Mache, D. H., Eqaivalence Theorem on Weighted SimultaneousL p-Approximation by the Method of Kantorovic Operators. J. Approx. Theory 77(1994), 351–363.

    MathSciNet  Google Scholar 

  10. Zhou, X. L., On Approximation of Continuous Functions by Szasz-Mirakjan Operators, J. Hangzhou Univ. 10(1983), 258–265.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Hebei Teachers University, 050016, Shijia zhuang Hebei, P. R. China

    Guo Shunsheng & Li Cuixiang

Authors
  1. Guo Shunsheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Li Cuixiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by NSF of Hebei Province.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shunsheng, G., Cuixiang, L. TheL p-saturation results weighted simultaneous approximation by the method of Bernstein-Durrmeyer operators. Approx. Theory & its Appl. 14, 78–89 (1998). https://doi.org/10.1007/BF02836932

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02836932

Keywords

Search

Navigation