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Convergence of the Bernstein–Durrmeyer Operators in Variation Seminorm

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Abstract

The aim of this paper is to study variation detracting property and convergence in variation of the Bernstein–Durrmeyer modifications of the classical Bernstein operators in the space of functions of bounded variation. These problems are studied with respect to the variation seminorm. Moreover we also study the rate of convergence in terms of total variation.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Arts, Abant Izzet Baysal University, Bolu, Turkey

    Harun Karsli

  2. Department of Mathematics, Faculty of Science, University of Ankara, Ankara, Turkey

    Özlem Öksüzer Yılık & Fatma Taşdelen Yeşildal

Authors
  1. Harun Karsli
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  2. Özlem Öksüzer Yılık
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  3. Fatma Taşdelen Yeşildal
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Correspondence to Özlem Öksüzer Yılık.

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Karsli, H., Öksüzer Yılık, Ö. & Taşdelen Yeşildal, F. Convergence of the Bernstein–Durrmeyer Operators in Variation Seminorm. Results Math 72, 1257–1270 (2017). https://doi.org/10.1007/s00025-017-0653-0

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  • DOI: https://doi.org/10.1007/s00025-017-0653-0

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