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

  • İbrahi̇m Çanak EMAIL logo and Ümi̇t Totur
Published/Copyright: April 1, 2015
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Abstract

Let (umns) 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 (umns) converges in Pringsheim's sense. We prove that (umns) converges in Pringsheim's sense if (umns) 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.

MSC: 40E05; 40B05

Prof. İbrahi̇m Çanak thanks very much Prof. Ümi̇t Totur, the principal author of the present paper, for his kind service as corresponding author.

Received: 2013-10-28
Accepted: 2014-6-2
Published Online: 2015-4-1
Published in Print: 2016-3-1

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