{"title":"关于cirric不动点定理的一些定性性质","authors":"Madalina Moga","doi":"10.24193/subbmath.2022.1.04","DOIUrl":null,"url":null,"abstract":"\"It is well known that of all the extensions of the Banach-Caccioppoli Contraction Principle, the most general result was established by \\'{C}iri\\'{c} in 1974. In this paper, we will present some results related to \\'{C}iri\\'{c} type operator in complete metric spaces. Existence and uniqueness are re-called and several stability properties (data dependence and Ostrowski stability property) are proved. Using the retraction-displacement condition, we will establish the well-posedness and the Ulam-Hyers stability property of the fixed point equation $x=f(x)$.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"50 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On some qualitative properties of Ciric's fixed point theorem\",\"authors\":\"Madalina Moga\",\"doi\":\"10.24193/subbmath.2022.1.04\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\\"It is well known that of all the extensions of the Banach-Caccioppoli Contraction Principle, the most general result was established by \\\\'{C}iri\\\\'{c} in 1974. In this paper, we will present some results related to \\\\'{C}iri\\\\'{c} type operator in complete metric spaces. Existence and uniqueness are re-called and several stability properties (data dependence and Ostrowski stability property) are proved. Using the retraction-displacement condition, we will establish the well-posedness and the Ulam-Hyers stability property of the fixed point equation $x=f(x)$.\\\"\",\"PeriodicalId\":30022,\"journal\":{\"name\":\"Studia Universitatis BabesBolyai Geologia\",\"volume\":\"50 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-03-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Studia Universitatis BabesBolyai Geologia\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24193/subbmath.2022.1.04\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Universitatis BabesBolyai Geologia","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24193/subbmath.2022.1.04","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On some qualitative properties of Ciric's fixed point theorem
"It is well known that of all the extensions of the Banach-Caccioppoli Contraction Principle, the most general result was established by \'{C}iri\'{c} in 1974. In this paper, we will present some results related to \'{C}iri\'{c} type operator in complete metric spaces. Existence and uniqueness are re-called and several stability properties (data dependence and Ostrowski stability property) are proved. Using the retraction-displacement condition, we will establish the well-posedness and the Ulam-Hyers stability property of the fixed point equation $x=f(x)$."