A new multi-step iterative algorithm for approximating common fixed points of a finite family of multi-valued Bregman relatively nonexpansive mappings
type: Item
instance of: scholarly article
title: A new multi-step iterative algorithm for approximating common fixed points of a finite family of multi-valued Bregman relatively nonexpansive mappings
zbMATH Open document ID: 1466.47043
author: Wiyada Kumam
author: Pongsakorn Sunthrayuth
author: Phond Phunchongharn
author: Khajonpong Akkarajitsakul
author: Parinya Sa Ngiamsunthorn
author: Poom Kumam
published in: Algorithms
publication date: 2019-03-26T00:00:00Z
review text: Summary: In this article, we introduce a new multi-step iteration for approximating a common fixed point of a finite class of multi-valued Bregman relatively nonexpansive mappings in the setting of reflexive Banach spaces. We prove a strong convergence theorem for the proposed iterative algorithm under certain hypotheses. Additionally, we also use our results for the solution of variational inequality problems and to find the zero points of maximal monotone operators. The theorems furnished in this work are new and well-established and generalize many well-known recent research works in this field.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 7042346
zbMATH Keywords: common fixed point
zbMATH Keywords: multi-valued Bregman relatively nonexpansive mapping
zbMATH Keywords: strong convergence
zbMATH Keywords: iterative methods
zbMATH Keywords: reflexive Banach spaces
zbMATH Keywords: variational inequality problems
zbMATH Keywords: maximal monotone
Wikidata QID: Q59306864
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a9020037
OpenAlex ID: W2407736079
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DOI: 10.3390/A9020037
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