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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 968492, 11 pages
http://dx.doi.org/10.1155/2013/968492
Research Article

Some Results on Fixed and Best Proximity Points of Multivalued Cyclic Self-Mappings with a Partial Order

Institute of Research and Development of Processes, University of Basque Country, Campus of Leioa (Bizkaia, Apatado) 644, 48080 Bilbao, Spain

Received 17 October 2012; Revised 7 March 2013; Accepted 22 March 2013

Academic Editor: Abdul Latif

Copyright © 2013 M. De la Sen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is devoted to investigate the fixed points and best proximity points of multivalued cyclic self-mappings on a set of subsets of complete metric spaces endowed with a partial order under a generalized contractive condition involving a Hausdorff distance. The existence and uniqueness of fixed points of both the cyclic self-mapping and its associate composite self-mappings on each of the subsets are investigated, if the subsets in the cyclic disposal are nonempty, bounded and of nonempty convex intersection. The obtained results are extended to the existence of unique best proximity points in uniformly convex Banach spaces.