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Some spaces of double sequences obtained through invariant mean and related concepts. (English) Zbl 1277.46003
Summary: We introduce some double sequence spaces involving the notions of invariant mean (or $\sigma$-mean) and $\sigma$-convergence for double sequences, while the idea of $\sigma$-convergence for double sequences was introduced by {\it C. Çakan} et al. [Appl. Math. Lett. 19, No. 10, 1122--1128 (2006; Zbl 1122.40004)] by using the notion of invariant mean. We determine here some inclusion relations and topological results for these new double sequence spaces.
##### MSC:
 46A45 Sequence spaces 40A05 Convergence and divergence of series and sequences 40B05 Multiple sequences and series
##### Keywords:
double sequence space
Full Text:
##### References:
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