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.