Tauberian theorems for statistically convergent double sequences
type: Item
instance of: scholarly article
title: Tauberian theorems for statistically convergent double sequences
zbMATH Open document ID: 1092.40002
author: Osama H. H. Edely
author: M. Mursaleen
published in: Information Sciences
publication date: 2006-03-28T00:00:00Z
review text: The authors consider two summability methods for real or complex double sequences \((x_{mn})\,.\) They mainly investigate the relation between statistical convergence and Cesàro \(C_{1,1}\)-conver\-gence and the relation of the two methods to convergence. They show that for bounded sequences Cesàro convergence is stronger than statistical convergence and furthermore that the condition \(| x_{mj}-x_{m,j-1}| \leq c/j\) together with the condition \(| x_{kn}-x_{k-1,n}| \leq c/k\) (uniformly in \(m,n\)) form a Tauberian condition from statistical convergence to convergence and from statistical convergence of the Cesàro mean to convergence. A related Tauberian theorem for the Cesàro method is well known.
reviewed by: Ulrich Stadtmüller
Mathematics Subject Classification ID: 40B05
Mathematics Subject Classification ID: 40E05
zbMATH DE Number: 5015634
zbMATH Keywords: statistical convergence
zbMATH Keywords: Cesàro convergence
zbMATH Keywords: Tauberian theorems
MaRDI profile type: Publication
full work available at URL: j.ins.2005.01.006
OpenAlex ID: W2072430304
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DOI: 10.1016/J.INS.2005.01.006
description: scientific article; zbMATH DE number 5015634