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Zbl 1204.40006
Çakalli, H.; Savaş, E.
Statistical convergence of double sequences in topological groups.
(English)
[J] J. Comput. Anal. Appl. 12, No. 2, 421-426 (2010). ISSN 1521-1398; ISSN 1572-9206/e

The idea of the statistical convergence of single sequences was first studied by {\it H. Fast} [Colloq. Math. 2, 241--244 (1951; Zbl 0044.33605)]. The idea of the statistical convergence of double sequences was first introduced by {\it E. Mursaleen} and {\it H. H. Osama} [J. Math. Anal. Appl. 288, No.1, 223--231 (2003; Zbl 1032.40001)]. Most of the existing works on statistical convergence have been restricted to real or complex sequences. The authors give an extension of statistical convergence of double sequences to topological groups and give some theorems in this general setting.
[Umit Totur (Aydin)]
MSC 2000:
*40J05 Summability in abstract structures
40A35

Keywords: statistical convergence; statistical Cauchy sequence; double sequence; double natural density

Citations: Zbl 0044.33605; Zbl 1032.40001

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