Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces

Abstract

This paper investigates properties of convergence of distances of p-cyclic contractions on the union of the p subsets of an abstract set X defining probabilistic metric spaces and Menger probabilistic metric spaces as well as the characterization of Cauchy sequences which converge to the best proximity points. The existence and uniqueness of fixed points and best proximity points of p-cyclic contractions defined in induced complete Menger spaces are also discussed in the case when the associate complete metric space is a uniformly convex Banach space. On the other hand, the existence and the uniqueness of fixed points of the p-composite mappings restricted to each of the p subsets in the cyclic disposal are also investigated and some illustrative examples are given.