{"title":"Some fixed-point theorems of convex orbital $(\\alpha, \\beta )$-contraction mappings in geodesic spaces","authors":"Rahul Shukla","doi":"10.1186/s13663-023-00749-8","DOIUrl":null,"url":null,"abstract":"Abstract The aim of this paper is to broaden the applicability of convex orbital $(\\alpha, \\beta )$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>(</mml:mo> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>β</mml:mi> <mml:mo>)</mml:mo> </mml:math> -contraction mappings to geodesic spaces. This class of mappings is a natural extension of iterated contraction mappings. The paper derives fixed-point theorems both with and without assuming continuity. Furthermore, the paper investigates monotone convex orbital $(\\alpha, \\beta )$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>(</mml:mo> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>β</mml:mi> <mml:mo>)</mml:mo> </mml:math> -contraction mappings and establishes a fixed-point theorem for this class of mappings.","PeriodicalId":87256,"journal":{"name":"Fixed point theory and algorithms for sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fixed point theory and algorithms for sciences and engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1186/s13663-023-00749-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
Abstract The aim of this paper is to broaden the applicability of convex orbital $(\alpha, \beta )$ (α,β) -contraction mappings to geodesic spaces. This class of mappings is a natural extension of iterated contraction mappings. The paper derives fixed-point theorems both with and without assuming continuity. Furthermore, the paper investigates monotone convex orbital $(\alpha, \beta )$ (α,β) -contraction mappings and establishes a fixed-point theorem for this class of mappings.