Quadruple Best Proximity Points with Applications to Functional and Integral Equations

Abstract

This manuscript is devoted to obtaining a quadruple best proximity point for a cyclic contraction mapping in the setting of ordinary metric spaces. The validity of the theoretical results is also discussed in uniformly convex Banach spaces. Furthermore, some examples are given to strengthen our study. Also, under suitable conditions, some quadruple fixed point results are presented. Finally, as applications, the existence and uniqueness of a solution to a system of functional and integral equations are obtained to promote our paper.

Untitled

“…The point x is called the best proximity (BPP(T ) of T : A → B, if d(x, T x) = d(A, B)), where {d(A, B) = inf d(x, y) : x ∈ A, y ∈ B}. Various best proximity point results were established on such spaces, for example, see [6,7,8] and references therein.…”