{"title":"Equivalents of Ordered Fixed Point Theorems of Kirk, Caristi, Nadler, Banach, and others","authors":"Sehie Park","doi":"10.31197/atnaa.1127248","DOIUrl":null,"url":null,"abstract":"Recently, we improved our long-standing Metatheorem in Fixed Point Theory. In this paper, as its applications, some well-known order theoretic fixed point theo- rems are equivalently formulated to existence theorems on maximal elements, com- mon fixed points, common stationary points, and others. Such theorems are the ones due to Banach, Nadler, Browder-Göhde-Kirk, Caristi-Kirk, Caristi, Brøndsted, and possibly many others.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"39 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in the Theory of Nonlinear Analysis and its Application","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31197/atnaa.1127248","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
Recently, we improved our long-standing Metatheorem in Fixed Point Theory. In this paper, as its applications, some well-known order theoretic fixed point theo- rems are equivalently formulated to existence theorems on maximal elements, com- mon fixed points, common stationary points, and others. Such theorems are the ones due to Banach, Nadler, Browder-Göhde-Kirk, Caristi-Kirk, Caristi, Brøndsted, and possibly many others.
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