Best Proximity Pair Theorems for Noncyclic Mappings in Banach and Metric Spaces

Let A and B be two nonempty subsets of a metric space X. A mapping T : A[B ! A[B is said to be noncyclic if T(A) A and T(B) B. For such a mapping, a pair (x; y) 2 A B such that Tx = x, Ty = y and d(x; y) = dist(A;B) is called a best proximity pair. In this paper we give some best proximity pair results for noncyclic mappings under certain contractive conditions.