On Existence and Uniqueness of g-Best Proximity Points under φ,θ,α,g-Contractivity Conditions and Consequences
We collect, improve, and generalize very recent results due to Mongkolkeha et al. (2014) in three directions: firstly, we study g-best proximity points; secondly, we employ more general test functions than can be found in that paper, which lets us prove best proximity results using different kinds o...
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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/10.1155/2014/234027 |
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| _version_ | 1832551848109670400 |
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| author | Poom Kumam Antonio Francisco Roldán López de Hierro |
| author_facet | Poom Kumam Antonio Francisco Roldán López de Hierro |
| author_sort | Poom Kumam |
| collection | DOAJ |
| description | We collect, improve, and generalize very recent results due to Mongkolkeha et al. (2014) in three directions: firstly, we study g-best proximity points; secondly, we employ more general test functions than can be found in that paper, which lets us prove best proximity results using different kinds of control functions; thirdly, we introduce and handle a weak version of the P-property. Our results can also be applied to the study of coincidence points between two mappings as a particular case. As a consequence, the contractive condition we introduce is more general than was used in the mentioned paper. |
| format | Article |
| id | doaj-art-f18b0b236ea74e938c86cd14ae01e5a6 |
| 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-f18b0b236ea74e938c86cd14ae01e5a62025-02-03T06:00:25ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/234027234027On Existence and Uniqueness of g-Best Proximity Points under φ,θ,α,g-Contractivity Conditions and ConsequencesPoom Kumam0Antonio Francisco Roldán López de Hierro1Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok 10140, ThailandDepartment of Mathematics, University of Jaén, Campus las Lagunillas, s/n, 23071 Jaén, SpainWe collect, improve, and generalize very recent results due to Mongkolkeha et al. (2014) in three directions: firstly, we study g-best proximity points; secondly, we employ more general test functions than can be found in that paper, which lets us prove best proximity results using different kinds of control functions; thirdly, we introduce and handle a weak version of the P-property. Our results can also be applied to the study of coincidence points between two mappings as a particular case. As a consequence, the contractive condition we introduce is more general than was used in the mentioned paper.http://dx.doi.org/10.1155/2014/234027 |
| spellingShingle | Poom Kumam Antonio Francisco Roldán López de Hierro On Existence and Uniqueness of g-Best Proximity Points under φ,θ,α,g-Contractivity Conditions and Consequences Abstract and Applied Analysis |
| title | On Existence and Uniqueness of g-Best Proximity Points under φ,θ,α,g-Contractivity Conditions and Consequences |
| title_full | On Existence and Uniqueness of g-Best Proximity Points under φ,θ,α,g-Contractivity Conditions and Consequences |
| title_fullStr | On Existence and Uniqueness of g-Best Proximity Points under φ,θ,α,g-Contractivity Conditions and Consequences |
| title_full_unstemmed | On Existence and Uniqueness of g-Best Proximity Points under φ,θ,α,g-Contractivity Conditions and Consequences |
| title_short | On Existence and Uniqueness of g-Best Proximity Points under φ,θ,α,g-Contractivity Conditions and Consequences |
| title_sort | on existence and uniqueness of g best proximity points under φ θ α g contractivity conditions and consequences |
| url | http://dx.doi.org/10.1155/2014/234027 |
| work_keys_str_mv | AT poomkumam onexistenceanduniquenessofgbestproximitypointsunderphthagcontractivityconditionsandconsequences AT antoniofranciscoroldanlopezdehierro onexistenceanduniquenessofgbestproximitypointsunderphthagcontractivityconditionsandconsequences |