Tauberian conditions under which statistical convergence follows from statistical summability by weighted mean method in two-normed spaces

Abstract

In this paper, we introduce the statistical summability by the weighted mean method in a two-normed space and establish necessary and sufficient Tauberian conditions under which statistical convergence of a sequence (x n ) follows from its statistical summability by weighted mean method in a two-normed space. In particular, our Tauberian conditions are satisfied if (x n ) is statistically slowly oscillating in a two-normed space. The main theorem of this paper is the statistical extension of a Tauberian theorem in C ¸anak et al. [Acta Comment. Univ. Tartu. Math. 24, 49-57 (2020)].