  For two nonempty, closed, bounded and convex subsets $A$ and $B$ of a
uniformly convex Banach space $X$ consider a mapping $T:(A \times B) \cup (B
\times A) \rightarrow A \cup B$ 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.
