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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 867203, 13 pages
http://dx.doi.org/10.1155/2012/867203
Research Article

A Kantorovich Type of Szasz Operators Including Brenke-Type Polynomials

Department of Mathematics, Faculty of Science, Ankara University, Tandoğan, 06100 Ankara, Turkey

Received 27 September 2012; Accepted 15 November 2012

Academic Editor: Abdelghani Bellouquid

Copyright © 2012 Fatma Taşdelen et al. 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

We give a Kantorovich variant of a generalization of Szasz operators defined by means of the Brenke-type polynomials and obtain convergence properties of these operators by using Korovkin's theorem. We also present the order of convergence with the help of a classical approach, the second modulus of continuity, and Peetre's -functional. Furthermore, an example of Kantorovich type of the operators including Gould-Hopper polynomials is presented and Voronovskaya-type result is given for these operators including Gould-Hopper polynomials.