Approximation by complex Lupaş–Durrmeyer polynomials based on Polya distribution

Abstract

The study of the generalization of the Bernstein and Bernstein–Durrmeyer polynomials attached to a continuous function $f:[0,1]\to \mathbb{R}$ and based on the Polya distribution were considered in some recent publications. The aim of the present note is to study the approximation properties of the complex version of these Durrmeyer-type operators, attached to analytic functions in a disk $D_R=\{z\in \mathbb{C};|z|<R\}$ with $R>1$.