A Continuation Method for Weakly Contractive Mappings under the Interior Condition
Recently, Frigon proved that, for weakly contractive maps, the property of having a fixed point is invariant by a certain class of homotopies, obtaining as a consequence a Leray-Schauder alternative for this class of maps in a Banach space. We prove here that the Leray-Schauder condition in the afor...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2009-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/2009/809315 |
| _version_ | 1818907570052530176 |
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| author | David Ariza-Ruiz Antonio Jiménez-Melado |
| author_facet | David Ariza-Ruiz Antonio Jiménez-Melado |
| author_sort | David Ariza-Ruiz |
| collection | DOAJ |
| description | Recently, Frigon proved that, for weakly contractive maps, the property of having a fixed point is invariant by a certain class of homotopies, obtaining as a consequence a Leray-Schauder alternative for this class of maps in a Banach space. We prove here that the Leray-Schauder condition in the aforementioned result can be replaced by a modification of it, the interior condition. We also show that our arguments work for a certain class of generalized contractions, thus complementing a result of Agarwal and O'Regan. |
| first_indexed | 2024-12-19T21:57:13Z |
| format | Article |
| id | doaj.art-e9f64073145346b5b56e6c42e79359f2 |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-12-19T21:57:13Z |
| publishDate | 2009-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Applications |
| spelling | doaj.art-e9f64073145346b5b56e6c42e79359f22022-12-21T20:04:15ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122009-01-01200910.1155/2009/809315A Continuation Method for Weakly Contractive Mappings under the Interior ConditionDavid Ariza-RuizAntonio Jiménez-MeladoRecently, Frigon proved that, for weakly contractive maps, the property of having a fixed point is invariant by a certain class of homotopies, obtaining as a consequence a Leray-Schauder alternative for this class of maps in a Banach space. We prove here that the Leray-Schauder condition in the aforementioned result can be replaced by a modification of it, the interior condition. We also show that our arguments work for a certain class of generalized contractions, thus complementing a result of Agarwal and O'Regan.http://dx.doi.org/10.1155/2009/809315 |
| spellingShingle | David Ariza-Ruiz Antonio Jiménez-Melado A Continuation Method for Weakly Contractive Mappings under the Interior Condition Fixed Point Theory and Applications |
| title | A Continuation Method for Weakly Contractive Mappings under the Interior Condition |
| title_full | A Continuation Method for Weakly Contractive Mappings under the Interior Condition |
| title_fullStr | A Continuation Method for Weakly Contractive Mappings under the Interior Condition |
| title_full_unstemmed | A Continuation Method for Weakly Contractive Mappings under the Interior Condition |
| title_short | A Continuation Method for Weakly Contractive Mappings under the Interior Condition |
| title_sort | continuation method for weakly contractive mappings under the interior condition |
| url | http://dx.doi.org/10.1155/2009/809315 |
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