Best proximity point theorem in higher dimensions with an application

	Best proximity point theorem in higher dimensions with an application
International Journal of Nonlinear Analysis and Applications
دوره 13، Special Issue for selected papers of ICDACT-2021، خرداد 2022، صفحه 97-108 اصل مقاله (374.69 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6335
نویسندگان
Saranan Mondal¹؛ Supriti Laha¹؛ Ankush Chanda^* ²
¹Department of Mathematics, National Institute of Technology, Durgapur, West Bengal, India
²Department of Mathematics, Vellore Institute of Technology, Vellore, India
چکیده
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.
کلیدواژه‌ها
$F_n$-contractions؛ best proximity points؛ $P$-property؛ weak $P$-property؛ $n$-tuple best proximity points
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