Quantitative estimates for a new complex Durrmeyer operator in compact disks

Abstract

In the recent years the extension of linear positive operators from real to complex domain is one of the interesting area of research. In this context, we present the exact order of simultaneous approximation and Voronovskaja kind results with quantitative estimate for a new type of complex Durrmeyer operator (different from those previously studied), attached to analytic functions in compact disks. In this way, we put in evidence the overconvergence phenomenon for this kind of Durrmeyer operator, namely the extensions of approximation properties with exact quantitative estimates, from the real interval [1/3,2/3] to compact disks in the complex plane.