Approximation by a Durrmeyer-type operator in compact disks

In this paper, the exact order of simultaneous approximation and Voronovskaja kind results with quantitative estimate for a new type of complex Durrmeyer polynomials, attached to analytic functions in compact disks are obtained. In this way, we put in evidence the overconvergence phenomenon for this kind of Durrmeyer polynomials, namely the extensions of approximation properties with exact quantitative estimates, from the real interval [0, 1] to compact disks in the complex plane.