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Estimates for the differences of positive linear operators and their derivatives

Abstract

The present paper deals with the estimate of the differences of certain positive linear operators and their derivatives. Oxur approach involves operators defined on bounded intervals, as Bernstein operators, Kantorovich operators, genuine Bernstein-Durrmeyer operators, and Durrmeyer operators with Jacobi weights. The estimates in quantitative form are given in terms of the first modulus of continuity. In order to analyze the theoretical results in the last section, we consider some numerical examples.

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Acknowledgments

We are very grateful to the referees for their highly valuable comments and remarks. Special thanks are due for the suggestions leading to inequality (5) and to the actual form of Lemma 4.1.

Funding

The work of the first author was financed by the Lucian Blaga University of Sibiu and Hasso Plattner Foundation research grants LBUS-IRG-2019-05.

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Correspondence to Ana-Maria Acu.

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Acu, AM., Raşa, I. Estimates for the differences of positive linear operators and their derivatives. Numer Algor 85, 191–208 (2020). https://doi.org/10.1007/s11075-019-00809-4

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  • DOI: https://doi.org/10.1007/s11075-019-00809-4

Keywords

  • Positive linear operators
  • Differences of operators
  • Bernstein operators
  • Durrmeyer operators
  • Kantorovich operators

Mathematics Subject Classification (2010)

  • 41A25
  • 41A36