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Perturbed Bernstein-type operators

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Abstract

The present paper deals with modifications of Bernstein, Kantorovich, Durrmeyer and genuine Bernstein–Durrmeyer operators. Some previous results are improved in this study. Direct estimates for these operators by means of the first and second modulus of continuity are given. Also the asymptotic formulas for the new operators are proved.

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Data Availability Statement

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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Acknowledgements

The first author acknowledges the support of Lucian Blaga University of Sibiu under research Grant LBUS-IRG-2020-06. The second one is grateful for the departmental facilities provided during his senior professorship at the University of Duisburg-Essen.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No.5-7, 550012, Sibiu, Romania

    Ana-Maria Acu

  2. Faculty of Mathematics, University of Duisburg-Essen, Bismarckstr. 90, 47057, Duisburg, Germany

    Heiner Gonska

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  1. Ana-Maria Acu
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  2. Heiner Gonska
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Correspondence to Ana-Maria Acu.

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Acu, AM., Gonska, H. Perturbed Bernstein-type operators. Anal.Math.Phys. 10, 49 (2020). https://doi.org/10.1007/s13324-020-00389-w

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  • DOI: https://doi.org/10.1007/s13324-020-00389-w

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