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

Manuel De la Sen | Zendy

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

Author(s) -

Manuel De la Sen

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/968492

Subject(s) - mathematics , fixed point , intersection (aeronautics) , regular polygon , uniqueness , bounded function , hausdorff distance , metric space , hausdorff space , order (exchange) , banach space , least fixed point , pure mathematics , fixed point theorem , combinatorics , discrete mathematics , schauder fixed point theorem , mathematical analysis , geometry , finance , engineering , economics , aerospace engineering , picard–lindelöf theorem

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

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