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The Scientific World Journal
Volume 2014, Article ID 437863, 8 pages
http://dx.doi.org/10.1155/2014/437863
Research Article

Weighted -Statistical Convergence for Sequences of Positive Linear Operators

1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh, Arunachal Pradesh 791 112, India

Received 3 May 2014; Accepted 15 June 2014; Published 1 July 2014

Academic Editor: M. Mursaleen

Copyright © 2014 S. A. Mohiuddine 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 introduce the notion of weighted -statistical convergence of a sequence, where represents the nonnegative regular matrix. We also prove the Korovkin approximation theorem by using the notion of weighted -statistical convergence. Further, we give a rate of weighted -statistical convergence and apply the classical Bernstein polynomial to construct an illustrative example in support of our result.