Approximation properties of complex genuine α–Bernstein‐Durrmeyer operators

Abstract

Herein, we propose a complex form of genuine Bernstein‐Durrmeyer type operators depending on a non‐negative real parameter α$$ \alpha $$. We present the quantitative upper bound, Voronovskaja type result and the exact order of approximation for the derivatives of the operators attached to analytic functions on compact disks. These results validate the extension of approximation properties of complex genuine α$$ \alpha $$–Bernstein‐Durrmeyer type operators from real intervals to compact disks in the complex plane.