The Bregman distance without the Bregman function. II
type: Item
instance of: scholarly article
zbMATH Open document ID: 1290.47058
author: Daniel Reem
published in: Contemporary Mathematics
publication date: 2012-09-05T00:00:00Z
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47N10
Mathematics Subject Classification ID: 49M30
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C26
zbMATH DE Number: 6077534
zbMATH Keywords: Bregman distance
zbMATH Keywords: weak-strong space
zbMATH Keywords: asymptotic fixed point
zbMATH Keywords: strongly nonexpansive mapping
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1090/conm/568/11284
OpenAlex ID: W4232135723
DOI: 10.1090/CONM/568/11284
title: The Bregman distance without the Bregman function. II
review text: A weak-strong space is defined as a tuple \((X,S,\mathbb{T},d)\) consisting of a metric space \((X,d)\), a nonempty set \(S\subseteq X\), and a topology \(\mathbb{T}\) on \(X\) related to the metric topology in a suitable way. An instance of a weak-strong space is a reflexive Banach space together with its weak topology and a convex subset. In the context of weak-strong spaces, the author defines an abstract notion of Bregman distance in an axiomatic way, thus not relying upon any given Bregman function, and introduces appropriate notions of asymptotic fixed points and strong nonexpansiveness for mappings \(T:S\longrightarrow S\). The main theorem is a convergence result to a common asymptotic fixed point of a finite collection of strongly nonexpansive mappings.NEWLINENEWLINEEditorial remark. Part I has appeared as [\textit{D. Reem}, ``The Bregman distance without the Bregman function'', preprint].NEWLINENEWLINEFor the entire collection see [Zbl 1241.00017].
reviewed by: Juan-Enrique Martínez-Legaz
description: scientific article; zbMATH DE number 6077534