{"title":"Total Asymptotically Nonexpansive Mappings and Generalized Variational Inclusion Problems: Algorithmic and Analytical Approach","authors":"J. Balooee, Shih-sen Chang, Min Liu, J. Yao","doi":"10.1080/01630563.2023.2209147","DOIUrl":null,"url":null,"abstract":"Abstract In this article, we pursue two goals. First, a new iterative scheme based on the resolvent operator method for finding a common element of the set of solutions of a generalized variational inclusion problem and the set of fixed points of a total asymptotically nonexpansive mapping in a real Banach space is constructed. Under some parameters controlling conditions, the strong convergence of the sequence generated by our proposed iterative algorithm to a common element of the above-mentioned two sets is proved. Our second purpose is to investigate and analyze the concept of H(.,.)-accretive operator that appeared in the literature and to point out some comments concerning it. Several new examples are also provided.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"906 - 953"},"PeriodicalIF":1.4000,"publicationDate":"2023-05-12","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/10.1080/01630563.2023.2209147","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 In this article, we pursue two goals. First, a new iterative scheme based on the resolvent operator method for finding a common element of the set of solutions of a generalized variational inclusion problem and the set of fixed points of a total asymptotically nonexpansive mapping in a real Banach space is constructed. Under some parameters controlling conditions, the strong convergence of the sequence generated by our proposed iterative algorithm to a common element of the above-mentioned two sets is proved. Our second purpose is to investigate and analyze the concept of H(.,.)-accretive operator that appeared in the literature and to point out some comments concerning it. Several new examples are also provided.
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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