Copyright © 2012 N. I. Mahmudov and M. Kara. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The order of simultaneous approximation and Voronovskaja-type results with quantitative estimate for complex q-Kantorovich polynomials () attached to analytic functions on compact disks are obtained. In particular, it is proved that for functions analytic in , , the rate of approximation by the q-Kantorovich operators () is of order versus for the classical Kantorovich operators.