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Approximation by Complex Perturbed Bernstein-Type Operators

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Abstract

In this paper we consider complex form of a modified (perturbed) Bernstein operators attached to an analytic function in a disk of radius \(R>1\) centered at the origin. We obtain quantitative estimates of the convergence in compact disks and exact degree of simultaneous approximation with the help of upper estimates in quantitative form, and of lower estimates obtained from a qualitative Voronovskaja type result.

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Acknowledgements

The authors are grateful to the anonymous reviewer for valuable suggestions which greatly improved this paper.

The work was done jointly, while the first author visited Ankara University during November 2-16, 2019, supported by The Scientific and Technological Research Council of Turkey, “2221 - Fellowships for Visiting Scientists and Scientists on Sabbatical Leave, with application number 1059B211900262”.

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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 Science, Department of Mathematics, Ankara University, 06100, Beşevler, Ankara, Turkey

    Gülen Başcanbaz-Tunca

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  1. Ana-Maria Acu
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  2. Gülen Başcanbaz-Tunca
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Correspondence to Gülen Başcanbaz-Tunca.

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Acu, AM., Başcanbaz-Tunca, G. Approximation by Complex Perturbed Bernstein-Type Operators. Results Math 75, 120 (2020). https://doi.org/10.1007/s00025-020-01244-x

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  • DOI: https://doi.org/10.1007/s00025-020-01244-x

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