Invariant mean and some core theorems for double sequences
type: Item
instance of: scholarly article
title: Invariant mean and some core theorems for double sequences
zbMATH Open document ID: 1209.40003
published in: Taiwanese Journal of Mathematics
publication date: 2010-05-14T00:00:00Z
review text: A bounded double sequence \(x=(x_{jk})\) of real numbers is said to be \(\sigma-\)convergent to a number \(L\) if \(x\in V_2^\sigma\) with \[ V_{2}^{\sigma}= \bigg\{x: \lim_{p,q\to \infty}\frac{1}{(p+1)(q+1)}\sum_{j=0}^p\sum_{k=0}^q x_{\sigma^j(s),\sigma^k(t)}=L\text{ uniformly in }s,t;\;L=\sigma-\lim x\bigg\}, \] where \(\sigma^p(k)\) denotes the \(p\)th iterate of the mapping \(\sigma\) at \(k\), and \(\sigma^p(k)\neq k\) for all integer \(k\geq 0\), \(p\geq1\). In this paper the authors define and characterize the class \((V_2^{\sigma},V_2^{\sigma})\) and establish a core theorem. They determine a Tauberian condition for core inclusion and core equivalence.
reviewed by: Umit Totur
Mathematics Subject Classification ID: 40C05
Mathematics Subject Classification ID: 40H05
Mathematics Subject Classification ID: 40B05
Mathematics Subject Classification ID: 40E05
zbMATH DE Number: 5707728
zbMATH Keywords: double sequence
zbMATH Keywords: \(p\)-convergence
zbMATH Keywords: invariant mean
zbMATH Keywords: \(\sigma\)-convergence
zbMATH Keywords: \(\sigma\)-core
zbMATH Keywords: core theorems
author: M. Mursaleen
author: S. A. Mohiuddine
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500405725
OpenAlex ID: W4210954224
DOI: 10.11650/TWJM/1500405725
description: scientific article; zbMATH DE number 5707728