{"title":"Interpolative fuzzy Z-contraction with its application to Fredholm non-linear integral equation","authors":"Shobha Jain, S. Radenović","doi":"10.56947/gjom.v14i1.1009","DOIUrl":null,"url":null,"abstract":"The aim of this paper is to introduce the notion of interpolative fuzzy Z-contractive condition for a pair of self maps in a fuzzy metric space, which enlarges, unifies and generalizes the existing fuzzy contractions (by Gregori and Sapena [6]), ψ contraction (by Mihet [11]), fuzzy Z-contractions (by Shukla et al. [21]) and Tirado contraction (by Tirado [22]), which are for only one self map. Using this, we establish a unique common fixed point theorem for two self maps satisfying condition (S), which was introduced by Shukla et al. in [21] through weak compatibility. As an applications, we discuss fixed point theorem for Fredholm non-linear integral equation. The article also includes an example, which shows the validity of our results.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Gulf Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56947/gjom.v14i1.1009","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The aim of this paper is to introduce the notion of interpolative fuzzy Z-contractive condition for a pair of self maps in a fuzzy metric space, which enlarges, unifies and generalizes the existing fuzzy contractions (by Gregori and Sapena [6]), ψ contraction (by Mihet [11]), fuzzy Z-contractions (by Shukla et al. [21]) and Tirado contraction (by Tirado [22]), which are for only one self map. Using this, we establish a unique common fixed point theorem for two self maps satisfying condition (S), which was introduced by Shukla et al. in [21] through weak compatibility. As an applications, we discuss fixed point theorem for Fredholm non-linear integral equation. The article also includes an example, which shows the validity of our results.
本文的目的是引入模糊度量空间中对自映射的插值模糊z -压缩条件的概念,它扩大、统一和推广了已有的只针对一个自映射的模糊压缩(Gregori和Sapena[6])、ψ压缩(Mihet[11])、模糊z -压缩(Shukla et al.[21])和Tirado压缩(Tirado[22])。利用这一点,我们建立了Shukla等人在[21]中通过弱相容引入的满足条件(S)的两个自映射的唯一公共不动点定理。作为应用,讨论了Fredholm非线性积分方程的不动点定理。文中还给出了一个算例,说明了我们的结果的有效性。