Tauberian Theorems for Sequences in 2-Normed Spaces

Abstract

In this paper we initiate the study of Tauberian theorems for sequences in 2-normed spaces. We introduce a necessary and sufficient Tauberian condition for (C, 1) summable sequences in such spaces. Corollaries allow this condition to be replaced by 2-normed analogues of Schmidt-type slow oscillation condition or Hardy-type two-sided condition.