Statistical convergence of double sequences in topological groups. (English) Zbl 1204.40006

Çakalli, H.; Savaş, E.

J. Comput. Anal. Appl. 12, No. 2, 421-426 (2010).

The idea of the statistical convergence of single sequences was first studied by H. Fast [Colloq. Math. 2, 241–244 (1951; Zbl 0044.33605)]. The idea of the statistical convergence of double sequences was first introduced by E. Mursaleen and 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.

Reviewer: Umit Totur (Aydin)

MSC:

40J05	Summability in abstract structures (should also be assigned at least one other classification number from Section 40-XX)
40A35	Ideal and statistical convergence

Keywords:

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