Tauberian Conditions for Double Sequences That Are Statistically Summable by Weighted Means

The concept of statistical convergence of ordinary (single) sequences was introduced by Fast in 1951. Basic properties of statistical convergence were proved by Schönberg and Fridy. Móricz extended the concept of statistical convergence from single to multiple sequences and proved some basic results. Móricz and Orhan have recently proved necessary and sufficient Tauberian conditions under which statistical convergence follows from statistical summability by weighted means. We extend this result from single to double sequences. 2000 Mathematics Subject Classification. 40B05, 40E05, 40G05