Two valued measure and summability of double sequences in asymmetric context
type: Item
instance of: scholarly article
title: Two valued measure and summability of double sequences in asymmetric context
zbMATH Open document ID: 1240.40031
author: Juan-Miguel Gracia
published in: Acta Mathematica Hungarica
publication date: 2011-02-25T00:00:00Z
review text: The distance function \(d\) in an asymmetric metric space \((X,d)\) satisfies \(d(x,y)\geq0\), \(d(x,y)=0\) iff \(x=y\), \(d(x,z)\leq d(x,y)+d(y,z)\), but \(d(x,y)\) need not be equal to \(d(y,x)\). Various kinds of convergence or divergence of double sequences are examined in asymmetric metric spaces satisfying a special ``approximate metric axiom'' (AMA) involving a function \(c(x,y)\) such that \(d(x,y)\leq c(x,y)d(y,x)\) for all \(x,y\) in \(X\) and some further boundedness restrictions. The ideas of the authors' earlier paper [Czech. Math. J. 59, 1141--1155 (2009; Zbl 1224.40009)] are extended to double sequences in AMA asymmetric metric spaces.
reviewed by: Gerald A. Heuer
Mathematics Subject Classification ID: 40J05
Mathematics Subject Classification ID: 40B05
Mathematics Subject Classification ID: 40A30
Mathematics Subject Classification ID: 40A05
zbMATH DE Number: 5857813
zbMATH Keywords: asymmetric metric space
zbMATH Keywords: approximate metric axiom (AMA)
zbMATH Keywords: double sequences
zbMATH Keywords: forward and backward \(\mu\)-statistical convergence/divergence/Cauchy condition
zbMATH Keywords: convergence/divergence/Cauchy condition in \(\mu\)-density
zbMATH Keywords: condition \((APO_2)\)
MaRDI profile type: Publication
full work available at URL: s10474-010-0005-y
OpenAlex ID: W2001332701
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DOI: 10.1007/S10474-010-0005-Y
description: scientific article; zbMATH DE number 5857813