A Continuation Method for Weakly Contractive Mappings under the Interior Condition

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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Main Authors: David Ariza-Ruiz, Antonio Jiménez-Melado
Format: Article
Language:English
Published: SpringerOpen 2009-01-01
Series:Fixed Point Theory and Applications
Online Access:http://dx.doi.org/10.1155/2009/809315
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spelling 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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