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Simultaneous approximation by a class of Bernstein-Durrmeyer operators preserving linear functions

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Abstract

We introduce and study a one-parameter class of positive linear operators constituting a link between the well-known operators of S.N. Bernstein and their genuine Bernstein-Durrmeyer variants. Several limiting cases are considered including one relating our operators to mappings investigated earlier by Mache and Zhou. A recursion formula for the moments is proved and estimates for simultaneous approximation of derivatives are given.

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Authors and Affiliations

  1. University of Duisburg-Essen, D-47048, Duisburg, Germany

    Heiner Gonska

  2. Transilvania University, RO-500036, Braşov, Romania

    Radu Păltănea

Authors
  1. Heiner Gonska
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  2. Radu Păltănea
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Correspondence to Heiner Gonska.

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Gonska, H., Păltănea, R. Simultaneous approximation by a class of Bernstein-Durrmeyer operators preserving linear functions. Czech Math J 60, 783–799 (2010). https://doi.org/10.1007/s10587-010-0049-8

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  • DOI: https://doi.org/10.1007/s10587-010-0049-8

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