{"title":"Generalized Enriched Nonexpansive Mappings and Their Fixed Point Theorems","authors":"Rahul Shukla, Rekha Panicker","doi":"10.1155/2023/5572893","DOIUrl":null,"url":null,"abstract":"This paper introduces a novel category of nonlinear mappings and provides several theorems on their existence and convergence in Banach spaces, subject to various assumptions. Moreover, we obtain convergence theorems concerning iterates of \n \n α\n \n -Krasnosel’skiĭ mapping associated with the newly defined class of mappings. Further, we present that \n \n α\n \n -Krasnosel’skiĭ mapping associated with \n \n b\n \n -enriched quasinonexpansive mapping is asymptotically regular. Furthermore, some new convergence theorems concerning \n \n b\n \n -enriched quasinonexpansive mappings have been proved.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":"70 3","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Abstract and Applied Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2023/5572893","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
This paper introduces a novel category of nonlinear mappings and provides several theorems on their existence and convergence in Banach spaces, subject to various assumptions. Moreover, we obtain convergence theorems concerning iterates of
α
-Krasnosel’skiĭ mapping associated with the newly defined class of mappings. Further, we present that
α
-Krasnosel’skiĭ mapping associated with
b
-enriched quasinonexpansive mapping is asymptotically regular. Furthermore, some new convergence theorems concerning
b
-enriched quasinonexpansive mappings have been proved.
期刊介绍：
Abstract and Applied Analysis is a mathematical journal devoted exclusively to the publication of high-quality research papers in the fields of abstract and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimization theory, and control theory. Abstract and Applied Analysis supports the publication of original material involving the complete solution of significant problems in the above disciplines. Abstract and Applied Analysis also encourages the publication of timely and thorough survey articles on current trends in the theory and applications of analysis.
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