Analysis in Theory and Applications

, Volume 21, Issue 3, pp 294–300 | Cite as

Approximation of a kind of Nevai-Durrmeyer operators inL w p spaces

  • Guanzhen Zhou


The present paper introduces a kind of Nevai-Durrmeyer operators which can be used to approximate functions in L w p spaces with the weight ω(x)=1/∝1−x 2, and the approximate rate is also estimated.

Key words

Nevai-Durrmeyer operator weighted Lp space Jackson estimate 

AMS(2000) subject classification

41A17 41A25 


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  1. [1]
    Della Vecchia, B., Uniform Approximation by Nevai Operators, J. Approx. Theory, 116(2002), 28–48.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Nevai, P., Orthogonal Polynomials, Mem. Amer. Math. Soc., 213(1979).Google Scholar
  3. [3]
    Della Vecchia, B. and Mastroianni, C., Pointwise Simultaneous Approximation by Rational Operators, J. Approx. Theory, 65(1991), 140–150.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Durrmeyer, J.L., Thèse de 3e Cycle, Faculté des Sciences de I’Université de Paris, 1967.Google Scholar
  5. [5]
    Heilmann, M.,L p-Saturation of Some Modified Bernstein Operators, J. Approx. Theory, 54(1988), 250–259.CrossRefMathSciNetGoogle Scholar
  6. [6]
    Berens, H. and Xu, Y., On Bernstein-Durrmeyer Polynomials with Jacobi Weights, preprint (1989).Google Scholar
  7. [7]
    Wang, Z. Y. and Shen, X. C., WeightedL p-Approximation by Modified Higher Order Hermite-Fejer Interpoltion, Adv. Math., 23(1994), 342–353.MATHMathSciNetGoogle Scholar
  8. [8]
    Yu, D. S. and Zhou, S. P., WeightedL p-approximation by the Modified Nevai Operators, Anal. Theory Appl., to appear.Google Scholar
  9. [9]
    Stein, E. M., Singular Integrals and Differentiablity of Functions, Princeton Univ. Press, 1970.Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • Guanzhen Zhou
    • 1
  1. 1.Department of MathematicsNingbo UniversityNingboP.R. China

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