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

Manuel De la Sen, Erdal Karapınar
2015 Journal of Function Spaces  
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 associate
more » ... te metric space is a uniformly convex Banach space. On the other hand, the existence and the uniqueness of fixed points of thep-composite mappings restricted to each of thepsubsets in the cyclic disposal are also investigated and some illustrative examples are given.
doi:10.1155/2015/470574 fatcat:44pn33n3nfan3hdjygagxw7dg4