Fahad Jahangeer, Salha Alshaikey, Umar Ishtiaq, Tania A. Lazăr, Vasile L. Lazăr, Liliana Guran
{"title":"Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications","authors":"Fahad Jahangeer, Salha Alshaikey, Umar Ishtiaq, Tania A. Lazăr, Vasile L. Lazăr, Liliana Guran","doi":"10.3390/fractalfract7100766","DOIUrl":null,"url":null,"abstract":"In this manuscript, we present several types of interpolative proximal contraction mappings including Reich–Rus–Ciric-type interpolative-type contractions and Kannan-type interpolative-type contractions in the setting of bipolar metric spaces. Further, taking into account the aforementioned mappings, we prove best proximity point results. These results are an extension and generalization of existing ones in the literature. Furthermore, we provide several nontrivial examples, an application to find the solution of an integral equation, and a nonlinear fractional differential equation to show the validity of the main results.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"80 1","pages":"0"},"PeriodicalIF":3.6000,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractal and Fractional","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/fractalfract7100766","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
In this manuscript, we present several types of interpolative proximal contraction mappings including Reich–Rus–Ciric-type interpolative-type contractions and Kannan-type interpolative-type contractions in the setting of bipolar metric spaces. Further, taking into account the aforementioned mappings, we prove best proximity point results. These results are an extension and generalization of existing ones in the literature. Furthermore, we provide several nontrivial examples, an application to find the solution of an integral equation, and a nonlinear fractional differential equation to show the validity of the main results.
在本文中，我们提出了几种类型的插值近端收缩映射，包括reich - rus - ciric型插值-型收缩和kannan型插值-型收缩。此外，考虑到上述映射，我们证明了最佳的接近点结果。这些结果是对已有文献结果的扩展和概括。此外，我们还提供了几个非平凡的例子，一个求积分方程解的应用，以及一个非线性分数阶微分方程来证明主要结果的有效性。
期刊介绍：
Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
