{"title":"A fixed point theorem for nonself nonlinear contractions in length spaces","authors":"Simeon Reich, A. Zaslavski","doi":"10.12775/tmna.2023.007","DOIUrl":null,"url":null,"abstract":"In 1988 N.A. Assad showed that a nonself nonlinear contraction taking a closed \nsubset of a complete metrically convex space into the space so that the boundary \nof this subset is mapped back into the subset itself has a unique fixed point.\n In the present paper we extend this result by replacing the complete metrically\n convex space with a complete metric space which is a length space.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topological Methods in Nonlinear Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.12775/tmna.2023.007","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In 1988 N.A. Assad showed that a nonself nonlinear contraction taking a closed
subset of a complete metrically convex space into the space so that the boundary
of this subset is mapped back into the subset itself has a unique fixed point.
In the present paper we extend this result by replacing the complete metrically
convex space with a complete metric space which is a length space.
期刊介绍:
Topological Methods in Nonlinear Analysis (TMNA) publishes research and survey papers on a wide range of nonlinear analysis, giving preference to those that employ topological methods. Papers in topology that are of interest in the treatment of nonlinear problems may also be included.