Coincidence Best Proximity Points in Convex Metric Spaces

Abstract

Let $T, S:A\cup B\to A\cup B$ be mappings such that $T(A)\subseteq B, T(B)\subseteq A$ and $S(A)\subseteq A, S(B)\subseteq B$. Then the pair $(T;S)$ of mapping defined on $A\cup B$ is called cyclic-noncyclic pair, where $A$ and $B$ are two nonempty subsets of a metric space $(X,d)$. A coincidence best proximity point $p\in A\cup B$ for such a pair of mappings $(T;S)$ is a point such that $d(Sp,Tp)=dist(A,B)$. In the current paper, we study the existence and convergence of coincidence best proximity points in the setting of convex metric spaces. We also present an application of our results to an integral equation.