Applications of Bregman-Opial property to Bregman nonspreading mappings in Banach spaces
type: Item
instance of: scholarly article
title: Applications of Bregman-Opial property to Bregman nonspreading mappings in Banach spaces
zbMATH Open document ID: 1428.47028
DOI: 10.1155/2014/272867
author: Eskandar Naraghirad
author: Ngai-Ching Wong
author: Jen-Chih Yao
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: The Opial property of Hilbert spaces and some other special Banach spaces is a powerful tool in establishing fixed point theorems for nonexpansive and, more generally, nonspreading mappings. Unfortunately, not every Banach space shares the Opial property. However, every Banach space has a similar Bregman-Opial property for Bregman distances. In this paper, using Bregman distances, we introduce the classes of Bregman nonspreading mappings and investigate the Mann and Ishikawa iterations for these mappings. We establish weak and strong convergence theorems for Bregman nonspreading mappings.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 7022063
zbMATH Keywords: Bregman-Opial property
zbMATH Keywords: Mann iteration
zbMATH Keywords: Ishikawa iteration
zbMATH Keywords: weak convergence
zbMATH Keywords: strong convergence
zbMATH Keywords: Bregman nonspreading mappings
Wikidata QID: Q59037423
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/272867
OpenAlex ID: W2090682043
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description: scientific article; zbMATH DE number 7022063