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International Journal of Mathematics and Mathematical Sciences
Volume 2014, Article ID 674159, 5 pages
http://dx.doi.org/10.1155/2014/674159
Research Article

Statistical Summability through de la Vallée-Poussin Mean in Probabilistic Normed Spaces

Department of Mathematics, Science and Art Faculty, Adiyaman University, 02040 Adiyaman, Turkey

Received 13 February 2014; Revised 31 March 2014; Accepted 1 April 2014; Published 16 April 2014

Academic Editor: Biren N. Mandal

Copyright © 2014 Ayhan Esi. 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

Two concepts—one of statistical convergence and the other of de la Vallée-Poussin mean—play an important role in recent research on summability theory. In this work we define a new type of summability methods and statistical completeness involving the ideas of de la Vallée-Poussin mean and statistical convergence in the framework of probabilistic normed spaces.