On coupled best proximity points and Ulam-Hyers stability

Abstract

For two nonempty, closed, bounded and convex subsets $A$ and $B$ of a uniformly convex Banach space $X$ consider a mapping $T:(A\times B)\cup (B\times A)\to A\cup B$ satisfying $T(A,B)\subset B$ and $T(B,A)\subset A$. In this paper the existence of a coupled best proximity point is established when $T$ is considered to be a p-cyclic contraction mapping and a p-cyclic nonexpansive mapping. The Ulam-Hyers stability of the best proximity point problem is also studied.

13 pages