Best proximity point theorem in higher dimensions with an application

Document Type : Research Paper

Authors

1 Department of Mathematics, National Institute of Technology, Durgapur, West Bengal, India

2 Department of Mathematics, Vellore Institute of Technology, Vellore, India

Abstract

In this article, we introduce the notion of $F_n$-contractions $T:A^n\rightarrow B$ in standard metric spaces and explore the possibility of certain approximation results for these mappings. We prove the existence and uniqueness of $n$-tuple ($n \geq 2$) best proximity points of $F_n$-contractions, not necessarily continuous, using the weak $P$-property in complete metric spaces. Additionally, suitable examples are presented to substantiate our main results. Moreover, we anticipate a fixed point result to prove the existence and uniqueness of the solution for a type of integral equation to elucidate our obtained theorems.

Keywords

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Volume 13, Special Issue for selected papers of ICDACT-2021
The link to the conference website is https://vitbhopal.ac.in/event/icdact_dec_21/
March 2022
Pages 97-108
  • Receive Date: 12 August 2021
  • Revise Date: 20 December 2021
  • Accept Date: 12 January 2022