Abstract and Applied Analysis

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

M. De la Sen

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 968492, 11 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393442739

Digital Object Identifier
doi:10.1155/2013/968492

Mathematical Reviews number (MathSciNet)
MR3055934

Zentralblatt MATH identifier
1273.54050

Citation

De la Sen, M. Some Results on Fixed and Best Proximity Points of Multivalued Cyclic Self-Mappings with a Partial Order. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 968492, 11 pages. doi:10.1155/2013/968492. https://projecteuclid.org/euclid.aaa/1393442739


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