Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces
This paper investigates properties of convergence of distances of p-cyclic contractions on the union of the p subsets of an abstract set X defining probabilistic metric spaces and Menger probabilistic metric spaces as well as the characterization of Cauchy sequences which converge to the best proxi...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/470574 |
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| _version_ | 1832552230636486656 |
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| author | Manuel De la Sen Erdal Karapınar |
| author_facet | Manuel De la Sen Erdal Karapınar |
| author_sort | Manuel De la Sen |
| collection | DOAJ |
| description | This paper investigates properties of convergence of distances of p-cyclic contractions on the union of the p subsets of an abstract set X defining probabilistic metric spaces and Menger probabilistic metric spaces as well as the characterization of Cauchy sequences which converge to the best proximity points. The existence and uniqueness of fixed points and best proximity points of p-cyclic contractions defined in induced complete Menger spaces are also discussed in the case when the associate complete metric space is a uniformly convex Banach space. On the other hand, the existence and the uniqueness of fixed points of the p-composite mappings restricted to each of the p subsets in the cyclic disposal are also investigated and some illustrative examples are given. |
| format | Article |
| id | doaj-art-746430b31a0449d6aa36006c46531da0 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-746430b31a0449d6aa36006c46531da02025-02-03T05:59:12ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/470574470574Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric SpacesManuel De la Sen0Erdal Karapınar1Institute of Research and Development of Processes IIDP, Faculty of Science and Technology, University of the Basque Country, P.O. Box 644 de Bilbao Barrio Sarriena, Leioa, 48940 Bizkaia, SpainDepartment of Mathematics, ATILIM University, Incek, 06836 Ankara, TurkeyThis paper investigates properties of convergence of distances of p-cyclic contractions on the union of the p subsets of an abstract set X defining probabilistic metric spaces and Menger probabilistic metric spaces as well as the characterization of Cauchy sequences which converge to the best proximity points. The existence and uniqueness of fixed points and best proximity points of p-cyclic contractions defined in induced complete Menger spaces are also discussed in the case when the associate complete metric space is a uniformly convex Banach space. On the other hand, the existence and the uniqueness of fixed points of the p-composite mappings restricted to each of the p subsets in the cyclic disposal are also investigated and some illustrative examples are given.http://dx.doi.org/10.1155/2015/470574 |
| spellingShingle | Manuel De la Sen Erdal Karapınar Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces Journal of Function Spaces |
| title | Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces |
| title_full | Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces |
| title_fullStr | Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces |
| title_full_unstemmed | Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces |
| title_short | Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces |
| title_sort | some results on best proximity points of cyclic contractions in probabilistic metric spaces |
| url | http://dx.doi.org/10.1155/2015/470574 |
| work_keys_str_mv | AT manueldelasen someresultsonbestproximitypointsofcycliccontractionsinprobabilisticmetricspaces AT erdalkarapınar someresultsonbestproximitypointsofcycliccontractionsinprobabilisticmetricspaces |