Abstract
Let A and B be two nonempty subsets of a metric space (X, d). A best proximity point of a non-self-mapping T : A -> B is a point x* is an element of A satisfying the equality d(x*,Tx*) = d(A, B), where d(A, B) = inf{d(a, b) : a is an element of A, b is an element of B}. In this paper, we introduce a new concept of alpha-psi-proximal contractive type mappings and establish best proximity point theorems for such mappings in complete metric spaces. Several applications and interesting consequences of our obtained results are presented. (C) 2013 Elsevier Masson SAS. All rights reserved.