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Statistical convergence of double sequences. (English) Zbl 1032.40001
Summary: The idea of statistical convergence was first introduced by H. Fast [Colloq. Math. 2, 241-244 (1951; Zbl 0044.33605)] but the rapid developments were started after the papers of J. A. Šalát [Math. Slovaca 30, 139-150 (1980; Zbl 0437.40003)] and J. A. Fridy [Analysis 5, 301-313 (1985; Zbl 0588.40001)]. Nowadays it has become one of the most active areas of research in the field of summability. In this paper we define and study statistical analogue of convergence and Cauchy for double sequences. We also establish the relation between statistical convergence and strongly Cesàro summable double sequences.

MSC:
40A05 Convergence and divergence of series and sequences
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