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Zbl 1032.40001
Mursaleen; Edely, Osama H.H.
Statistical convergence of double sequences. (English)
[J] J. Math. Anal. Appl. 288, No.1, 223-231 (2003). ISSN 0022-247X

Summary: The idea of statistical convergence was first introduced by {\it H. Fast} [Colloq. Math. 2, 241-244 (1951; Zbl 0044.33605)] but the rapid developments were started after the papers of {\it J. A. Šalát} [Math. Slovaca 30, 139-150 (1980; Zbl 0437.40003)] and {\it 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 2000:: *40A05 Convergence of series and sequences

Keywords: Statistical convergence; Statistically Cauchy sequence; Double sequence; Double natural density

Citations: Zbl 0044.33605; Zbl 0437.40003; Zbl 0588.40001

Cited in: Zbl 1204.40006 Zbl 1135.40002 Zbl 1224.40009 Zbl 1147.54016 Zbl 1132.40312 Zbl 1084.40001

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