Amnay Amri, Mohamed Amine Khamsi, Osvaldo D. Méndez
{"title":"A Fixed Point Theorem in the Lebesgue Spaces of Variable Integrability Lp(·)","authors":"Amnay Amri, Mohamed Amine Khamsi, Osvaldo D. Méndez","doi":"10.3390/sym15111999","DOIUrl":null,"url":null,"abstract":"We establish a fixed point property for the Lebesgue spaces with variable exponents Lp(·), focusing on the scenario where the exponent closely approaches 1. The proof does not impose any additional conditions. In particular, our investigation centers on ρ-non-expansive mappings defined on convex subsets of Lp(·), satisfying the “condition of uniform decrease” that we define subsequently.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symmetry-Basel","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/sym15111999","RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0
Abstract
We establish a fixed point property for the Lebesgue spaces with variable exponents Lp(·), focusing on the scenario where the exponent closely approaches 1. The proof does not impose any additional conditions. In particular, our investigation centers on ρ-non-expansive mappings defined on convex subsets of Lp(·), satisfying the “condition of uniform decrease” that we define subsequently.
期刊介绍:
Symmetry (ISSN 2073-8994), an international and interdisciplinary scientific journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced.