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Journal of Applied Mathematics
Volume 2012, Article ID 454579, 14 pages
http://dx.doi.org/10.1155/2012/454579
Research Article

Approximation Theorems for Generalized Complex Kantorovich-Type Operators

Eastern Mediterranean University, Gazimagusa, T.R. North Cyprus, Mersiin 10, Turkey

Received 28 April 2012; Accepted 3 September 2012

Academic Editor: Jinyun Yuan

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.