A fixed point theorem in probabilistic metric spaces with a convex structure

Abstract

The inequality Ffx;fy(qs) Fx;y(s) (s 0), where q 2 (0; 1), is generalized for multi- valued mappings in many directions. Using Hausdor distance S.B. Nadler in [7] intro- duced a generalization of Banach contraction principle in metric spaces. In [3] the de nition of probabilistic Nadler q-contraction is given. Using some results given in [12] a xed point theorem on spaces with a convex structure is obtained. Some xed point theorems in such spaces are proved in [1, 2].