Umar Ishtiaq, Fahim Ud Din, Khaleel Ahmad, Doha A. Kattan, I. Argyros
{"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}
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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.
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