Results in Mathematics

, 74:40 | Cite as

Approximation and Geometric Properties of Complex \(\alpha \)-Bernstein Operator

  • Nursel ÇetinEmail author


In this paper, we consider the complex form of a new generalization of the Bernstein operator, depending on a non-negative real parameter. We obtain quantitative upper estimate for simultaneous approximation, a qualitative Voronovskaja type result and the exact order of approximation. Also, we present some shape preserving properties of the complex \(\alpha \)-Bernstein operator such as univalence, starlikeness, convexity and spirallikeness.


Complex Bernstein operator \(\alpha \)-Bernstein operator simultaneous approximation Voronovskaja type result order of approximation univalence starlikeness convexity spirallikeness 

Mathematics Subject Classification

30E10 41A25 41A28 30C45 



The author is grateful to the referees for making valuable suggestions, improving essentially the quality of the paper.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Research DepartmentTurkish State Meteorological ServiceAnkaraTurkey

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