APPROXIMATION BY Q-DURRMEYER - STANCU POLYNOMIALS IN COMPACT DISKS IN THE CASE OF Q > 1

Abstract

In this paper, the order of simultaneous approximation and Voronovskaja-type results with quantitative estimate for complex q-Kantorovich polynomials (q > 0) attached to analytic functions on compact disks are obtained. In particular, it is proved that for functions analytic in {z epsilon C : vertical bar z vertical bar < R}, R > q, the rate of approximation by the q-Durrmeyer - Stancu operators (q > 1) is of order q(-n) versus 1/n for the classical q-Durrmeyer - Stancu operators.