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Asymptotic Expansions for Bernstein–Durrmeyer–Chlodovsky Polynomials

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Abstract

We define a Durrmeyer variant of the Bernstein–Chlodovsky polynomials and study its rate of convergence. The main result is a complete asymptotic expansion. As a special case we obtain a Voronovskaja-type formula.

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Acknowledgements

The authors are very grateful to the anonymous referees for an extremely thorough reading of the manuscript. The valuable hints led to several improvements of the paper.

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Authors and Affiliations

  1. Technische Hochschule Mittelhessen, Fachbereich MND, Wilhelm-Leuschner-Straße 13, 61169, Friedberg, Germany

    Ulrich Abel

  2. Department of Mathematics, Faculty of Science and Arts, Abant Izzet Baysal University, Gölköy-Bolu, Turkey

    Harun Karsli

Authors
  1. Ulrich Abel
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  2. Harun Karsli
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Correspondence to Ulrich Abel.

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Abel, U., Karsli, H. Asymptotic Expansions for Bernstein–Durrmeyer–Chlodovsky Polynomials. Results Math 73, 104 (2018). https://doi.org/10.1007/s00025-018-0863-0

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  • DOI: https://doi.org/10.1007/s00025-018-0863-0

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