Statistical Convergence of Double Sequences on Probabilistic Normed Spaces

Karakus, S.; Demırcı, K.

doi:https://doi.org/10.1155/2007/14737

International Journal of Mathematics and Mathematical Sciences

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Research Article | Open Access

Volume 2007 | Article ID 014737 | https://doi.org/10.1155/2007/14737

Statistical Convergence of Double Sequences on Probabilistic Normed Spaces

S. Karakus¹and K. Demırcı¹

Academic Editor: Rodica D. Costin

Received07 Nov 2006

Accepted26 Apr 2007

Published14 Jun 2007

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.

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Copyright

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.

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