Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces. (19th May 2015)

• Record Type: Journal Article
• Authors: De la Sen, Manuel; Karapınar, Erdal
• Other Names: Vetro Calogero Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2015(2015)
• Publication Date: 2015-05-19
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2015/470574
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : This paper investigates properties of convergence of distances ofp -cyclic contractions on the union of thep subsets of an abstract setX 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 ofp -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 thep -composite mappings restricted to each of thep subsets in the cyclic disposal are also investigated and some illustrative examples are given.