Umar Ishtiaq, Fahim Ud Din, Khaleel Ahmad, Doha A. Kattan, I. Argyros
{"title":"广义𝜃-Contraction的不动点结果","authors":"Umar Ishtiaq, Fahim Ud Din, Khaleel Ahmad, Doha A. Kattan, I. Argyros","doi":"10.3390/foundations3030028","DOIUrl":null,"url":null,"abstract":"Any two points are close together in a Θ-contraction by a factor of Θ. The function Δ is implied to be a contraction under this condition, but with a tighter bound on the contraction factor. In this paper, we introduce the notions of orthogonal Θ-contraction and orthogonal α−Θ-contraction and prove several fixed point results by utilizing these contraction mappings in the context of orthogonal metric spaces. Further, we provide several non-trivial examples to show the validity of our results.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"228 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fixed Point Results for Generalized 𝜃-Contraction\",\"authors\":\"Umar Ishtiaq, Fahim Ud Din, Khaleel Ahmad, Doha A. Kattan, I. Argyros\",\"doi\":\"10.3390/foundations3030028\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Any two points are close together in a Θ-contraction by a factor of Θ. The function Δ is implied to be a contraction under this condition, but with a tighter bound on the contraction factor. In this paper, we introduce the notions of orthogonal Θ-contraction and orthogonal α−Θ-contraction and prove several fixed point results by utilizing these contraction mappings in the context of orthogonal metric spaces. Further, we provide several non-trivial examples to show the validity of our results.\",\"PeriodicalId\":81291,\"journal\":{\"name\":\"Foundations\",\"volume\":\"228 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-07-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Foundations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3390/foundations3030028\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Foundations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/foundations3030028","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Any two points are close together in a Θ-contraction by a factor of Θ. The function Δ is implied to be a contraction under this condition, but with a tighter bound on the contraction factor. In this paper, we introduce the notions of orthogonal Θ-contraction and orthogonal α−Θ-contraction and prove several fixed point results by utilizing these contraction mappings in the context of orthogonal metric spaces. Further, we provide several non-trivial examples to show the validity of our results.
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