Approximation by genuine q-bernstein-durrmeyer polynomials in compact disKS

Abstract

In this paper, the order of simultaneous approximation and Voronovskaja type theorems with quantitative estimate for complex genuine q-Bernstein-Durrmeyer polynomials (0 < q < 1) attached to analytic functions on compact disks are obtained. Our results show that extension of the complex genuine q-Bernstein-Durrmeyer polyno-mials from real intervals to compact disks in the complex plane extends approximation properties (with quantitative estimates).