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Statistical Convergence of Double Sequences on Probabilistic Normed Spaces

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  • S. Karakus
  • K. Demırcı

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.

Suggested Citation

  • S. Karakus & K. Demırcı, 2007. "Statistical Convergence of Double Sequences on Probabilistic Normed Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2007, pages 1-11, June.
    • Handle: RePEc:hin:jijmms:014737
    DOI: 10.1155/2007/14737
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    Cited by:

    1. Mursaleen, M. & Mohiuddine, S.A., 2009. "Statistical convergence of double sequences in intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2414-2421.
    2. Mausumi Sen & Pradip Debnath, 2011. "Statistical convergence in intuitionistic fuzzy n-normed linear spaces," Fuzzy Information and Engineering, Springer, vol. 3(3), pages 259-273, September.

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