Skip to main content
SpringerLink
Log in

Pointwise Simultaneous Approximation by Combinations of Baskakov Operators

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

Abstract

In this paper, we investigate the relation between the rate of convergence for the derivatives of the combinations of Baskakov operators and the smoothness for the derivatives of the functions approximated. We give some direct and inverse results on pointwise simultaneous approximation by the combinations of Baskakov operators. We also give a new equivalent result on pointwise approximation by these 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. Becker, M.: Global approximation theorems for Sz´asz–Mirakjan and Baskakov operators in polynomial weight spaces. Indiana Univ. Math. J., 27, 127–142 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  2. Totik, V.: Uniform approximation by Baskakov and Meyer–K¨onig and Zeller operators. Periodica Math. Hungar, 14, 209–228 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  3. Felten, M.: Local and global approximation theorems for positive linear operators. J. Approx. Theory, 94, 396–419 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Xie, L. S.: Direct and inverse theorems for Baskakov operators and their derivatives. Chin. Ann. of Math., 21A, 253–260 (2000)

    Google Scholar 

  5. Ditzian, Z., Jiang, D.: Approximation of functions by polynomials in C[-1, 1]. Canad. J. Math., 44, 924–940 (1992)

    MATH  MathSciNet  Google Scholar 

  6. Ditzian, Z., Jiang, D., Leviatan D.: Simultaneous polynomial approximation. SIAM J. Math. Anal., 24, 1652–1661 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  7. Ditzian, Z., Totik, V.: Moduli of Smoothness, Springer-Verlag, New York, 1987

  8. Xie, L. S., Zhang, X. P.: Pointwise characterization for combinations of Baskakov operators. Approx. Theory and Its Appl., 18(2), 76–89 (2002)

    MATH  Google Scholar 

  9. Zhang, X. P., Xie, L. S.: Equivalence theorem on simultaneous approximation by combination of Baskakov operators. Math. Appl., 16(2), 54–58 (2003)

    MATH  Google Scholar 

  10. Xie, L. S.: Pointwise approximation theorems for combinations and derivatives of Baskakov operators. J. Nanjing Univ. Math. Biquarterly, 18(2), 251–260 (2001)

    MATH  Google Scholar 

  11. Berens, H., Lorentz, G. G.: Inverse theorems for Bernstein polynomials. Indiana Univ. Math. J., 21, 693–708 (1972)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai 200444, P. R.China

    Lin Sen Xie

  2. Department of Mathematics, Lishui University, Lishui 323000, P. R. China

    Lin Sen Xie

  3. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China

    Zhong Rui Shi

Authors
  1. Lin Sen Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhong Rui Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lin Sen Xie.

Additional information

This research is supported by the National Natural Science Foundation of China and the Zhejiang Provincial Natural Science Foundation of China

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xie, L.S., Shi, Z.R. Pointwise Simultaneous Approximation by Combinations of Baskakov Operators. Acta Math Sinica 23, 935–944 (2007). https://doi.org/10.1007/s10114-005-0827-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-005-0827-7

Keywords

MR (2000) Subject Classification

Search

Navigation