Some Properties of Distances and Best Proximity Points of Cyclic Proximal Contractions in Metric Spaces
This paper presents some results concerning the properties of distances and existence and uniqueness of best proximity points of p-cyclic proximal, weak proximal contractions, and some of their generalizations for the non-self-mapping T:⋃i∈p-Ai→⋃i∈p-Bi (p≥2), where Ai and Bi, ∀i∈p-={1,2,…,p}, are n...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/914915 |
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| author | M. De La Sen Asier Ibeas |
| author_facet | M. De La Sen Asier Ibeas |
| author_sort | M. De La Sen |
| collection | DOAJ |
| description | This paper presents some results concerning the properties of distances and existence and uniqueness of best proximity points of p-cyclic proximal, weak proximal contractions, and some of their generalizations for the non-self-mapping T:⋃i∈p-Ai→⋃i∈p-Bi (p≥2), where Ai and Bi, ∀i∈p-={1,2,…,p}, are nonempty subsets of X which satisfy TAi⊆Bi,∀i∈p-, such that (X,d) is a metric space. The boundedness and the convergence of the sequences of distances in the domains and in their respective image sets of the cyclic proximal and weak cyclic proximal non-self-mapping, and of some of their generalizations are investigated. The existence and uniqueness of the best proximity points and the properties of convergence of the iterates to such points are also addressed. |
| format | Article |
| id | doaj-art-1e265db3e4e04d6e8b784b3e4d9f0cf7 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1e265db3e4e04d6e8b784b3e4d9f0cf72025-02-03T06:44:37ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/914915914915Some Properties of Distances and Best Proximity Points of Cyclic Proximal Contractions in Metric SpacesM. De La Sen0Asier Ibeas1Institute of Research and Development of Processes, Campus of Leioa (Bizkaia), University of the Basque Country, P.O. Box 644 Bilbao, Barrio Sarriena, 48940 Leioa, SpainDepartment of Telecommunications and Systems Engineering, Autonomous University of Barcelona, Bellaterra, 08193 Barcelona, SpainThis paper presents some results concerning the properties of distances and existence and uniqueness of best proximity points of p-cyclic proximal, weak proximal contractions, and some of their generalizations for the non-self-mapping T:⋃i∈p-Ai→⋃i∈p-Bi (p≥2), where Ai and Bi, ∀i∈p-={1,2,…,p}, are nonempty subsets of X which satisfy TAi⊆Bi,∀i∈p-, such that (X,d) is a metric space. The boundedness and the convergence of the sequences of distances in the domains and in their respective image sets of the cyclic proximal and weak cyclic proximal non-self-mapping, and of some of their generalizations are investigated. The existence and uniqueness of the best proximity points and the properties of convergence of the iterates to such points are also addressed.http://dx.doi.org/10.1155/2014/914915 |
| spellingShingle | M. De La Sen Asier Ibeas Some Properties of Distances and Best Proximity Points of Cyclic Proximal Contractions in Metric Spaces Abstract and Applied Analysis |
| title | Some Properties of Distances and Best Proximity Points of Cyclic Proximal Contractions in Metric Spaces |
| title_full | Some Properties of Distances and Best Proximity Points of Cyclic Proximal Contractions in Metric Spaces |
| title_fullStr | Some Properties of Distances and Best Proximity Points of Cyclic Proximal Contractions in Metric Spaces |
| title_full_unstemmed | Some Properties of Distances and Best Proximity Points of Cyclic Proximal Contractions in Metric Spaces |
| title_short | Some Properties of Distances and Best Proximity Points of Cyclic Proximal Contractions in Metric Spaces |
| title_sort | some properties of distances and best proximity points of cyclic proximal contractions in metric spaces |
| url | http://dx.doi.org/10.1155/2014/914915 |
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