Some classical Tauberian theorems for (C,1,1,1) summable triple sequences

Abstract

Abstract Let ( u m n s ) ${(u_{mns})}$ be a (C,1,1,1) summable triple sequence of real numbers. We give one-sided Tauberian conditions of Landau and Hardy type under which ( u m n s ) ${(u_{mns})}$ converges in Pringsheim's sense. We prove that ( u m n s ) ${(u_{mns})}$ converges in Pringsheim's sense if ( u m n s ) ${(u_{mns})}$ is slowly oscillating in certain senses. Moreover, we extend a Tauberian theorem given by Móricz [Studia Math. 110 (1994), 83–96] for double sequences to triple sequences.