International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 14737, 11 pages
doi:10.1155/2007/14737
Research Article
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.