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A continuation method for weakly contractive mappings under the interior condition

 

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Opened Access A continuation method for weakly contractive mappings under the interior condition
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Author: Ariza Ruiz, David
Jiménez Melado, Antonio
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2009
Published in: Fixed Point Theory and Applications, 2009, 1-8.
Document type: Article
Abstract: 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.
Cite: Ariza Ruiz, D. y Jiménez Melado, A. (2009). A continuation method for weakly contractive mappings under the interior condition. Fixed Point Theory and Applications, 2009, 1-8.
Size: 176.9Kb
Format: PDF

URI: http://hdl.handle.net/11441/42602

DOI: http://dx.doi.org/10.1155/2009/809315

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