%0 Journal Article
%T Best proximity point theorem in higher dimensions with an application
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Mondal, Saranan
%A Laha, Supriti
%A Chanda, Ankush
%D 2022
%\ 03/01/2022
%V 13
%N Special Issue for selected papers of ICDACT-2021
%P 97-108
%! Best proximity point theorem in higher dimensions with an application
%K $F_n$-contractions
%K best proximity points
%K $P$-property
%K weak $P$-property
%K $n$-tuple best proximity points
%R 10.22075/ijnaa.2022.6335
%X 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.
%U https://ijnaa.semnan.ac.ir/article_6335_eb8129ea83975aa6489305342fd86c96.pdf