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

Some classical Tauberian theorems for ( C ,1,1,1) summable triple sequences 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

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

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Publisher
de Gruyter
Copyright
Copyright © 2016 by the
ISSN
1072-947X
eISSN
1572-9176
DOI
10.1515/gmj-2015-0007
Publisher site
See Article on Publisher Site

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.

Journal

Georgian Mathematical Journal – de Gruyter

Published: Mar 1, 2016

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