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


ÇANAK İ. , Totur U.

GEORGIAN MATHEMATICAL JOURNAL, vol.23, no.1, pp.33-42, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.1515/gmj-2015-0007
  • Title of Journal : GEORGIAN MATHEMATICAL JOURNAL
  • Page Numbers: pp.33-42

Abstract

Let (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(mns)) converges in Pringsheim's sense. We prove that (u(mns)) converges in Pringsheim's sense if (u(mns)) is slowly oscillating in certain senses. Moreover, we extend a Tauberian theorem given by Moricz [11] for double sequences to triple sequences.