{"title":"Convergence theorem for an intermixed iteration in $p$-uniformly convex metric space","authors":"Kanyanee Saechou, A. Kangtunyakarn","doi":"10.37193/cjm.2023.02.09","DOIUrl":null,"url":null,"abstract":"In this paper, we first introduce the intermixed algorithm in $p$-uniformly convex metric spaces, and then we prove $\\Delta$-convergence of the proposed iterative method for finding a common element of the sets of fixed points of finite families of nonexpansive mappings in the framework of complete $p$-uniformly convex metric spaces. Furthermore, we apply our main theorem to prove $\\Delta$-convergence to solve the minimization problems in the framework of complete $p$-uniformly convex metric spaces. Finally, we give two examples in $L^p$ spaces and numerical examples to support our main results.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Carpathian Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.37193/cjm.2023.02.09","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we first introduce the intermixed algorithm in $p$-uniformly convex metric spaces, and then we prove $\Delta$-convergence of the proposed iterative method for finding a common element of the sets of fixed points of finite families of nonexpansive mappings in the framework of complete $p$-uniformly convex metric spaces. Furthermore, we apply our main theorem to prove $\Delta$-convergence to solve the minimization problems in the framework of complete $p$-uniformly convex metric spaces. Finally, we give two examples in $L^p$ spaces and numerical examples to support our main results.
期刊介绍:
Carpathian Journal of Mathematics publishes high quality original research papers and survey articles in all areas of pure and applied mathematics. It will also occasionally publish, as special issues, proceedings of international conferences, generally (co)-organized by the Department of Mathematics and Computer Science, North University Center at Baia Mare. There is no fee for the published papers but the journal offers an Open Access Option to interested contributors.