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This paper investigates properties of convergence of distances ofp-cyclic contractions on the union of thepsubsets of an abstract setXdefining 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 ofp-cyclic contractions defined in induced complete Menger spaces are also discussed in the case when the associatedoi:10.1155/2015/470574 fatcat:44pn33n3nfan3hdjygagxw7dg4