Some results on best proximity points of cyclic alpha-psi contractions in Menger probabilistic metric spaces

This paper investigates properties of convergence of distances of p-cyclic α-ψ-type contractions on the unio‎n of the p subsets of a space X defining probabilistic metric spaces and Menger spaces. The paper also investigates the characterization of both Cauchy and G-Cauchy sequences which are convergent, in particular, to best proximity points. On the other hand, the existence and uniqueness of fixed points and best proximity points of p-cyclic α-ψ-type contractions are also investigated. The fixed points of the p-composite self-mappings, which are obtained from the p-cyclic self-mapping restricted to each of the p subsets in the cyclic disposal, are also investigated while a generalization and some illustrative examples are also given.