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

Abstract

We introduce some double sequences 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 Çakan 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.