Approximation and Geometric Properties of Complex $$\alpha $$ α -Bernstein Operator

Abstract

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.