Statistical σ-Convergence of Double Sequences with Application

The concepts of sigma-statistical convergence, statistical sigma-convergence and strong sigma(q)-convergence of single (ordinary) sequences have been introduced and studied in [M. Mursaleen, O. H. H. Edely, On the invariant mean and statistical convergence, App. Math. Lett. 22, (2011), 1700-1704] which were obtained by unifying the notions of density and invariant mean. In this paper, we extend these ideas from single to double sequences. We also use the concept of statistical sigma-convergence of double sequences to prove a Korovkin-type approximation theorem for functions of two variables and give an example to show that our Korovkin-type approximation theorem is stronger than those proved earlier by other authors.