BEST PROXMITY POINT FOR CERTAIN NONLINEAR CONTRACTIONS IN MENGER PROBABLISTIC METRIC SPACES

Let A and B be nonempty subsets of a Menger probabilistic metric space with no common point and h: A → B be a non-self mapping. Taking into account the fact that given any element x ∈ A, F_x,hx(t) can be at most FA,B(t), for all t 0, the best proximity point theorems establish a global maximum of function x → F_x,hx(t), for all t 0 by imposing an approximate solution of the equation hx = x. In this article we derive best proximity point theorems for some non-self mappings and some cyclic mappings with special conditions and then we give suitable examples to display the validity of hypotheses of our results.