Tauberian theorems via the generalized Nörlund mean for sequences in 2-normed spaces

Abstract

. In this paper, we will show Tauberian conditions under which ordinary convergence of the sequence ( 𝑥 𝑛 ) in 2-normed space 𝑋 , follows from 𝑇 𝑝,𝑞𝑛 -summability. In fact we give a necessary and sufficient Tauberian condition for this method of summability. Also, we prove that Tauberian Theorems for these summability methods are valid with Schmidt-type slowly oscillating condition as well as with Hardy-type “big O” condition.