Advertisement

Approximation Theory and its Applications

, Volume 18, Issue 2, pp 90–101 | Cite as

The convergence rate of Multi-Bernstein-Durrmeyer operators with Jacobi weights

  • Xuan Peicai
  • Wang Jianli
  • You Gongqiang
  • Song Ruying
Article
  • 13 Downloads

Abstract

In this paper, we will consider the convergence rate of Multi-Bernstein-Durrmeyer operators with Jacobi weights and characterizations of approximation rate by means of a new K-functional.

Keywords

Linear Combination Convergence Rate Acta Math Approximation Rate Type Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Ditzian, Z. and Ivanov, K., Bernstein-Type Operators and Their Derivations, J. Approx. Theory, 56(1989), 72–89.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Zhang, Z. Q., On Weight Approximation of Bernstein Operators, Approx. Theory and Its Appli., 9(1993), No. 3, 61–72.Google Scholar
  3. [3]
    Heilmann, M.,L p-Satoration of Some Modified Bernstein Operators, J. Approx. Theory, 53 (1988), 260–273.CrossRefMathSciNetGoogle Scholar
  4. [4]
    Ditzian, Z. and Totik, V., Moduli of Smoothness, Speringer, 1987.Google Scholar
  5. [5]
    Grundmann, A., Inverse Theorem for Kanotorovich Polynomials, in “Fourier Analysis and Approximation Theory”, North-Holland, Amsterdam, 1978, 395–401.Google Scholar
  6. [6]
    Zhou, D. X., Inverse Theorem for Multidimensional Bernstein-Durrmeyer Operators inL p J. Approx. Theory, 70(1992), 68–93.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Xuan, P. C., On Weighted Approximation for a Class of Multidimensional Linear Positive Operators inL p, Acta Math. Appl. Sinica, 19(1996), No. 3, 370–384.MathSciNetGoogle Scholar
  8. [8]
    Xuan, P. C., On Weighted Approximation by Baskakov Type Operators, China Anna Math., 16A:5(1995), 614–624.MathSciNetGoogle Scholar
  9. [9]
    Xuan, P. C., On Weighted Approximation by Szász-Mirakjan Type Operators, Math. Num. Sinica, 4(1995), 427–442.MathSciNetGoogle Scholar
  10. [10]
    Xuan, P. C. and Zhou, D. X., Rate of Convergence for Baskakov Operators with jacobi-Weights, Acta Math. Appl. Sinics, 18(1995), No. 1, 129–139.MATHMathSciNetGoogle Scholar

Copyright information

© Springer 2002

Authors and Affiliations

  • Xuan Peicai
    • 1
  • Wang Jianli
    • 1
  • You Gongqiang
    • 1
  • Song Ruying
    • 2
  1. 1.Department of MathematicsShaoxing College of Arts and SciencesShaoxing, ZhejiangPRC
  2. 2.Department of MathematicsZhejiang UniversityHangzhou, ZhejiangPRC

Personalised recommendations