A. Ansar, Syamsuddin Mas'ud
{"title":"Fixed point results in α, β partial b-metric spaces using C-contraction type mapping and its generalization","authors":"A. Ansar, Syamsuddin Mas'ud","doi":"10.21580/jnsmr.2022.8.2.12778","DOIUrl":null,"url":null,"abstract":"Banach contraction mapping has main role in nonlinear analysis courses and has been modified to get new kind of generalizations in some abstract spaces to produce many fixed point theory. Fixed point theory has been proved in partial metric spaces and b-metric spaces as generalizations of metric spaces to obtain new theorems. In addition, using modified of contraction mapping we get some fixed point that have been used to solve differential equations or integral equations, and have many applications. Therefore, this area is actively studied by many researchers. The goal of this article is present and prove some fixed point theorems for extension of contraction mapping in α, β partial b-metric spaces. In this research, we learn about notions of b-metric spaces and partial metric that are combined to generated partial b-metric spaces from many literatures. Afterwards, generalizations are made to get α, β partial b-metric spaces. Using the properties of convergence, Cauchy sequences, and notions of completeness in α, β partial b-metric spaces, we prove some fixed point theorem. Fixed point theory that we generated used C-contraction mapping and its generalizations with some conditions. Existence and uniqueness of fixed point raised for some restrictions of α, β conditions. Some corollaries of main results are also proved. Our main theorems extend and increase some existence in the previous results.©2022 JNSMR UIN Walisongo. All rights reserved.","PeriodicalId":191192,"journal":{"name":"Journal of Natural Sciences and Mathematics Research","volume":"39 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Natural Sciences and Mathematics Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21580/jnsmr.2022.8.2.12778","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
利用c收缩型映射及其推广在α, β偏b-度量空间中的不动点结果
Banach收缩映射在非线性分析课程中占有重要的地位,它在一些抽象空间中得到了新的推广,从而产生了许多不动点理论。作为度量空间的推广,在偏度量空间和b度量空间中证明了不动点理论,得到了新的定理。此外,利用对收缩映射的修正得到了一些不动点,这些不动点已被用于求解微分方程或积分方程,并有许多应用。因此,这一领域受到许多研究者的积极研究。给出并证明了α, β偏b-度量空间中收缩映射扩展的不动点定理。在本研究中,我们从许多文献中了解了b-度量空间和偏度量空间的概念,并将它们组合起来生成偏b-度量空间。然后,推广得到α, β偏b-度量空间。利用α、β偏b-度量空间中的收敛性、柯西序列和完备性的概念,证明了一些不动点定理。利用c -收缩映射及其在一定条件下的推广,得到了不动点理论。给出了α、β条件下不动点的存在唯一性。并对主要结果的一些推论进行了证明。我们的主要定理扩展并增加了先前结果的存在性。©2022 JNSMR UIN Walisongo。版权所有。
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