Some spaces of double sequences obtained through invariant mean and related concepts (Q369996)

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 \textit{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.