Article
A continuation method for weakly contractive mappings under the interior condition
Author/s | Ariza Ruiz, David
Jiménez Melado, Antonio |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2009 |
Deposit Date | 2016-06-22 |
Published in |
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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 ... 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. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España Junta de Andalucía |
Project ID. | MTM2007-60854
FQM210 FQM1504 |
Citation | 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. |
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