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Statistical convergence of double sequences on probabilistic normed spaces. (English) Zbl 1147.54016
The authors discuss problems of statistical convergence for double sequences with respect to the probabilistic norm. This notion is introduced as a generalization of the concept of statistical convergence for double sequences [M. Mursaleen and O. H. H. Edely, J. Math. Anal. Appl. 288, No. 1, 223–231 (2003; Zbl 1032.40001)]. Similarly the authors define the notion of statistical Cauchy double sequences with respect to the given probabilistic norm. The authors demonstrate also that statistical convergence of double sequences on probabilistic normed spaces has some arithmetical properties similar to properties of the usual convergence for real points.

MSC:
54E70 Probabilistic metric spaces
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
46S50 Functional analysis in probabilistic metric linear spaces
40A05 Convergence and divergence of series and sequences
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