Some Spaces of Double Sequences Obtained through Invariant Mean and Related Concepts

S A Mohiuddine,Abdullah Alotaibi

doi:10.1155/2013/507950

Abstract

We introduce some double sequences spaces involving the notions of invariant mean (or -mean) and -convergence for double sequences while the idea of -convergence for double sequences was introduced by Cakan et al. 2006, by using the notion of invariant mean. We determine here some inclusion relations and topological results for these new double sequence spaces.

Highlights

Let us denote by Vσ the space of σ-convergent double sequences x =
For σ(n) = n + 1, the set Vσ is reduced to the set F of almost convergent double sequences [10]
We define and study some new spaces involving the idea of invariant mean and σ-convergence for double sequences and establish a relation between these spaces

Summary

Introduction

Let us denote by Vσ the space of σ-convergent double sequences x = (xjk). A bounded double sequence x = (xjk) is said to be strongly σ-convergent if there exists a number l such that Let us denote by [Vσ] the set of all strongly σ-convergent sequences x = (xjk). We define and study some new spaces involving the idea of invariant mean and σ-convergence for double sequences and establish a relation between these spaces.

Results

Conclusion