Tauberian theorems for double sequences that are statistically summable \((C,1,1)\)
type: Item
instance of: scholarly article
title: Tauberian theorems for double sequences that are statistically summable \((C,1,1)\)
zbMATH Open document ID: 1028.40002
DOI: 10.1016/S0022-247X(03)00529-8
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-11-16T00:00:00Z
review text: The author considers real and complex double sequences \((x_{jk})\) and compares statistical convergence and statistical convergence of their Cesàro means \((C,1,1) .\) For a bounded sequence \((x_{jk})\) statistical convergence to a limit \(s\) implies statistical convergence of its Cesàro means to the same limit. The two main results of the present paper give necessary and sufficient conditions, respectively two-sided Tauberian conditions for the reverse implication. The Tauberian conditions given are statistical versions of certain slow oscillation conditions. The results extend corresponding theorems by the author from ordinary sequences to double sequences; see \textit{F. Móricz} [J. Math. Anal. Appl. 275, 277-287 (2002; Zbl 1021.40002)].
Mathematics Subject Classification ID: 40E05
zbMATH DE Number: 2003911
zbMATH Keywords: double sequences
zbMATH Keywords: Pringshein convergence
zbMATH Keywords: statistical convergence
zbMATH Keywords: Cesàro means
zbMATH Keywords: Tauberian results
zbMATH Keywords: statistical slow oscillation
author: Ferenc Móricz
reviewed by: Ulrich Stadtmüller
MaRDI profile type: Publication
cites work: THE STATISTICAL AND STRONG p-CESARO CONVERGENCE OF SEQUENCES
cites work: Sur la convergence statistique
cites work: ON STATISTICAL CONVERGENCE
cites work: Statistical extensions of some classical Tauberian theorems
cites work: Tauberian conditions, under which statistical convergence follows from statistical summability \((C,1)\)
cites work: Statistical convergence of multiple sequences
cites work: The Integrability of Certain Functions and Related Summability Methods
full work available at URL: s0022-247x(03)00529-8
OpenAlex ID: W2054761823
description: scientific article; zbMATH DE number 2003911