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...
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2009-01-01
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Series: | Fixed Point Theory and Applications |
Online Access: | http://dx.doi.org/10.1155/2009/809315 |
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doaj-e9f64073145346b5b56e6c42e79359f22020-11-25T01:30:19ZengSpringerOpenFixed 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 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
David Ariza-Ruiz Antonio Jiménez-Melado |
spellingShingle |
David Ariza-Ruiz Antonio Jiménez-Melado A Continuation Method for Weakly Contractive Mappings under the Interior Condition Fixed Point Theory and Applications |
author_facet |
David Ariza-Ruiz Antonio Jiménez-Melado |
author_sort |
David Ariza-Ruiz |
title |
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_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_sort |
continuation method for weakly contractive mappings under the interior condition |
publisher |
SpringerOpen |
series |
Fixed Point Theory and Applications |
issn |
1687-1820 1687-1812 |
publishDate |
2009-01-01 |
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. |
url |
http://dx.doi.org/10.1155/2009/809315 |
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