{"title":"Fixed-Point Theorems Involving Small Lipschitz","authors":"C. R. Indrati","doi":"10.1155/2023/5236150","DOIUrl":null,"url":null,"abstract":"The small Lipschitz is a generalization of the Lipschitz condition. The Lipschitz condition guarantees the uniqueness of the solution of the initial value problems. A special Lipschitz condition in the small is a contraction in the small. Based on the small Lipschitz in this paper, fixed-point theorems involving contraction in the small will be presented. The results will be applied to develop Picard’s theorem.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-04-22","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/10.1155/2023/5236150","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
The small Lipschitz is a generalization of the Lipschitz condition. The Lipschitz condition guarantees the uniqueness of the solution of the initial value problems. A special Lipschitz condition in the small is a contraction in the small. Based on the small Lipschitz in this paper, fixed-point theorems involving contraction in the small will be presented. The results will be applied to develop Picard’s theorem.
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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