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Convergence Properties of Genuine Bernstein–Durrmeyer Operators

  • Ana-Maria AcuEmail author
Chapter

Abstract

The genuine Bernstein–Durrmeyer operators have notable approximation properties, and many papers have been written on them. In this paper, we introduce a modified genuine Bernstein–Durrmeyer operators. Some approximation results, which include local approximation, error estimation in terms of the modulus of continuity and weighted approximation is obtained. Also, a quantitative Voronovskaya-type approximation will be studied. The convergence of these operators to certain functions is shown by illustrative graphics using MAPLE algorithms.

Keywords

Genuine Bernstein–Durrmeyer operators Rate of convergence Linear positive operators Voronovskaja-type theorem 

2010 MSC

41A10 41A25 41A36 

Notes

Acknowledgements

The work was financed from Lucian Blaga University of Sibiu research grants LBUS-IRG-2017-03.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsLucian Blaga University of SibiuSibiuRomania

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