International Journal of Nonlinear Analysis and Applications
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 2022Pages 97-108
- Receive Date: 12 August 2021
- Revise Date: 20 December 2021
- Accept Date: 12 January 2022