On Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered -Metric Spaces
Two concepts—one of the coupled fixed point and the other of the generalized metric space—play a very active role in recent research on the fixed point theory. The definition of coupled fixed point was introduced by Bhaskar and Lakshmikantham (2006) while the generalized metric space was introduced...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/897198 |
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| _version_ | 1850173114215825408 |
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| author | S. A. Mohiuddine Abdullah Alotaibi |
| author_facet | S. A. Mohiuddine Abdullah Alotaibi |
| author_sort | S. A. Mohiuddine |
| collection | DOAJ |
| description | Two concepts—one of the coupled fixed point and the other of the generalized metric space—play a very active role in recent research on the fixed point theory. The definition of coupled fixed point was introduced by Bhaskar and Lakshmikantham (2006) while the generalized metric space was introduced by Mustafa and Sims (2006). In this work, we determine some coupled fixed point theorems for mixed monotone mapping satisfying nonlinear contraction in the framework of generalized metric space endowed with partial order. We also prove the uniqueness of the coupled fixed point for such mappings in this setup. |
| format | Article |
| id | doaj-art-d187f4be15ed4c488ffb52e31bf787fc |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d187f4be15ed4c488ffb52e31bf787fc2025-08-20T02:19:55ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/897198897198On Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered -Metric SpacesS. A. Mohiuddine0Abdullah Alotaibi1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaTwo concepts—one of the coupled fixed point and the other of the generalized metric space—play a very active role in recent research on the fixed point theory. The definition of coupled fixed point was introduced by Bhaskar and Lakshmikantham (2006) while the generalized metric space was introduced by Mustafa and Sims (2006). In this work, we determine some coupled fixed point theorems for mixed monotone mapping satisfying nonlinear contraction in the framework of generalized metric space endowed with partial order. We also prove the uniqueness of the coupled fixed point for such mappings in this setup.http://dx.doi.org/10.1155/2012/897198 |
| spellingShingle | S. A. Mohiuddine Abdullah Alotaibi On Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered -Metric Spaces Abstract and Applied Analysis |
| title | On Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered -Metric Spaces |
| title_full | On Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered -Metric Spaces |
| title_fullStr | On Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered -Metric Spaces |
| title_full_unstemmed | On Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered -Metric Spaces |
| title_short | On Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered -Metric Spaces |
| title_sort | on coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces |
| url | http://dx.doi.org/10.1155/2012/897198 |
| work_keys_str_mv | AT samohiuddine oncoupledfixedpointtheoremsfornonlinearcontractionsinpartiallyorderedmetricspaces AT abdullahalotaibi oncoupledfixedpointtheoremsfornonlinearcontractionsinpartiallyorderedmetricspaces |