Berinde-Borcut Tripled Best Proximity Points with Generalized Contraction Pairs

Premyuda Dechboon, Parinya Sa Ngiamsunthorn, Poom Kumam, Parin Chaipunya

Abstract

Given a pair of mappings F is a function from A^{3} to B and G is a function from B^{3} to A where A and B are nonempty subsets of a metric space X. We propose an existence theoremfor a best proximity point for this pair of mappings by assuming a generalized contractivity condition. We also show that their best proximity points carry acyclic interrelationship in the following sense: the mapping (u, v, w) in  A^{3} having a relation with (F(u, v, w), F(v, u, v), F(w, v, u )) in B^{3} maps a best proximity point of F to a best proximity point of G, and vice versa.