Tauberian conditions under which statistical convergence follows from statistical summability by weighted mean method in two-normed spaces
Articles > Article · 2023
Authors: İbrahim ÇANAK, Hülya Bakicierler
Miskolc Mathematical Notes, Journal Indexed in SCI Expanded, International, WoS, 2023, vol 24, pp 699-699
Summary
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.