Abstract and Applied Analysis
Volume 2012 (2012), Article ID 754217, 16 pages
http://dx.doi.org/10.1155/2012/754217
Research Article

Approximation by the -Szász-Mirakjan Operators

N. I. Mahmudov

Department of Mathematics, Eastern Mediterranean University, Gazimagusa, North Cyprus, Mersin 10, Turkey

Received 6 September 2012; Accepted 4 December 2012

Academic Editor: Behnam Hashemi

Copyright © 2012 N. I. Mahmudov. 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

This paper deals with approximating properties of the q-generalization of the Szász-Mirakjan operators in the case . Quantitative estimates of the convergence in the polynomial-weighted spaces and the Voronovskaja's theorem are given. In particular, it is proved that the rate of approximation by the q-Szász-Mirakjan operators ( ) is of order versus 1/n for the classical Szász-Mirakjan operators.