International Journal of Mathematics and Mathematical Sciences
Volume 2007, Article ID 14737, 11 pages
http://dx.doi.org/10.1155/2007/14737
Statistical Convergence of Double Sequences on Probabilistic Normed Spaces
Department of Mathematics, Faculty of Arts and Sciences, Sinop University, Sinop 57000, Turkey
Received 7 November 2006; Accepted 26 April 2007
Academic Editor: Rodica D. Costin
Copyright © 2007 S. Karakus and K. Demırcı. 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 concept of statistical convergence was presented by Steinhaus in 1951. This concept was extended to the double sequences by Mursaleen and Edely in 2003. Karakus has recently introduced the concept of statistical convergence of ordinary (single) sequence on probabilistic normed spaces. In this paper, we define statistical analogues of convergence and Cauchy for double sequences on probabilistic normed spaces. Then we display an exampl e such that our method of convergence is stronger than usual convergence on probabilistic normed spaces. Also we give a useful characterization for statistically convergent double sequences.