{"title":"Diametrically Relatively Nonexpansive Mappings and a Characterization of Proximal Normal Structure","authors":"R. Gholipour, M. Gabeleh, H. Mazaheri","doi":"10.1080/01630563.2023.2212495","DOIUrl":null,"url":null,"abstract":"Abstract We consider a new type of cyclic (noncyclic) mappings, called diametrically relatively nonexpansive maps which contains properly the class of cyclic (noncyclic) relatively nonexpansive mappings. For such mappings we obtain existence results of best proximity points (pairs) in the framework of Busemann convex spaces and generalize the recent conclusions in this direction. We also present a characterization of proximal normal structure in term of best proximity points (pairs) for diametrically relatively nonexpansive mappings.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"815 - 840"},"PeriodicalIF":1.4000,"publicationDate":"2023-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Functional Analysis and Optimization","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/01630563.2023.2212495","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract We consider a new type of cyclic (noncyclic) mappings, called diametrically relatively nonexpansive maps which contains properly the class of cyclic (noncyclic) relatively nonexpansive mappings. For such mappings we obtain existence results of best proximity points (pairs) in the framework of Busemann convex spaces and generalize the recent conclusions in this direction. We also present a characterization of proximal normal structure in term of best proximity points (pairs) for diametrically relatively nonexpansive mappings.
期刊介绍：
Numerical Functional Analysis and Optimization is a journal aimed at development and applications of functional analysis and operator-theoretic methods in numerical analysis, optimization and approximation theory, control theory, signal and image processing, inverse and ill-posed problems, applied and computational harmonic analysis, operator equations, and nonlinear functional analysis. Not all high-quality papers within the union of these fields are within the scope of NFAO. Generalizations and abstractions that significantly advance their fields and reinforce the concrete by providing new insight and important results for problems arising from applications are welcome. On the other hand, technical generalizations for their own sake with window dressing about applications, or variants of known results and algorithms, are not suitable for this journal.
Numerical Functional Analysis and Optimization publishes about 70 papers per year. It is our current policy to limit consideration to one submitted paper by any author/co-author per two consecutive years. Exception will be made for seminal papers.
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