Some Results on Fixed and Best Proximity Points of Multivalued Cyclic Self-Mappings with a Partial Order
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 fix...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/968492 |
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| author | M. De la Sen |
| author_facet | M. De la Sen |
| author_sort | M. De la Sen |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a6daff9710514d049b4fcf08a2d0ed4a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a6daff9710514d049b4fcf08a2d0ed4a2025-02-03T05:45:58ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/968492968492Some Results on Fixed and Best Proximity Points of Multivalued Cyclic Self-Mappings with a Partial OrderM. De la Sen0Institute of Research and Development of Processes, University of Basque Country, Campus of Leioa (Bizkaia, Apatado) 644, 48080 Bilbao, SpainThis 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.http://dx.doi.org/10.1155/2013/968492 |
| spellingShingle | M. De la Sen Some Results on Fixed and Best Proximity Points of Multivalued Cyclic Self-Mappings with a Partial Order Abstract and Applied Analysis |
| title | Some Results on Fixed and Best Proximity Points of Multivalued
Cyclic Self-Mappings with a Partial Order |
| title_full | Some Results on Fixed and Best Proximity Points of Multivalued
Cyclic Self-Mappings with a Partial Order |
| title_fullStr | Some Results on Fixed and Best Proximity Points of Multivalued
Cyclic Self-Mappings with a Partial Order |
| title_full_unstemmed | Some Results on Fixed and Best Proximity Points of Multivalued
Cyclic Self-Mappings with a Partial Order |
| title_short | Some Results on Fixed and Best Proximity Points of Multivalued
Cyclic Self-Mappings with a Partial Order |
| title_sort | some results on fixed and best proximity points of multivalued cyclic self mappings with a partial order |
| url | http://dx.doi.org/10.1155/2013/968492 |
| work_keys_str_mv | AT mdelasen someresultsonfixedandbestproximitypointsofmultivaluedcyclicselfmappingswithapartialorder |