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Approximation by Complex Bernstein-Durrmeyer Polynomials in Compact Disks

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Abstract

In this paper, the order of simultaneous approximation and Voronovskaja kind results with quantitative estimate for complex Bernstein-Durrmeyer polynomials attached to analytic functions on compact disks are obtained. In this way, we put in evidence the overconvergence phenomenon for Bernstein-Durrmeyer polynomials, namely the extensions of approximation properties (with quantitative estimates) from real intervals to compact disks in the complex plane.

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Authors and Affiliations

  1. Department of Mathematical Sciences, The University of Memphis, Memphis, TN, 38152, U.S.A.

    George A. Anastassiou

  2. Department of Mathematics and Computer Science, University of Oradea, Str. Armatei Romane 5, 410087, Oradea, Romania

    S. G. Gal

Authors
  1. George A. Anastassiou
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  2. S. G. Gal
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Corresponding author

Correspondence to George A. Anastassiou.

Additional information

This paper was written during the 2009 Spring Semester when the second author was a Visiting Professor at the Department of Mathematical Sciences, The University of Memphis, TN, U.S.A.

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Anastassiou, G.A., Gal, S.G. Approximation by Complex Bernstein-Durrmeyer Polynomials in Compact Disks. Mediterr. J. Math. 7, 471–482 (2010). https://doi.org/10.1007/s00009-010-0036-1

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  • DOI: https://doi.org/10.1007/s00009-010-0036-1

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