{"title":"非线性收缩控制函数的新类别及其应用","authors":"M. Berzig","doi":"10.31197/atnaa.1134524","DOIUrl":null,"url":null,"abstract":"We initiate the use of sub and super homogeneous control functions for nonlinear contractions in complete metric spaces and establish new fixed point theorems. Moreover, we develop other variants of control functions for the fixed point theorems of Boyd-Wong [2] and Matkowski [3]. As application, we present new sufficient conditions ensuring the existence of solutions to some classes of integral equations of Fredholm and Volterra type.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"4 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"New classes of control functions for nonlinear contractions and applications\",\"authors\":\"M. Berzig\",\"doi\":\"10.31197/atnaa.1134524\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We initiate the use of sub and super homogeneous control functions for nonlinear contractions in complete metric spaces and establish new fixed point theorems. Moreover, we develop other variants of control functions for the fixed point theorems of Boyd-Wong [2] and Matkowski [3]. As application, we present new sufficient conditions ensuring the existence of solutions to some classes of integral equations of Fredholm and Volterra type.\",\"PeriodicalId\":7440,\"journal\":{\"name\":\"Advances in the Theory of Nonlinear Analysis and its Application\",\"volume\":\"4 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-11-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"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.1134524\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in the Theory of Nonlinear Analysis and its Application","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31197/atnaa.1134524","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
New classes of control functions for nonlinear contractions and applications
We initiate the use of sub and super homogeneous control functions for nonlinear contractions in complete metric spaces and establish new fixed point theorems. Moreover, we develop other variants of control functions for the fixed point theorems of Boyd-Wong [2] and Matkowski [3]. As application, we present new sufficient conditions ensuring the existence of solutions to some classes of integral equations of Fredholm and Volterra type.
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