Ariza Ruiz, DavidJiménez Melado, Antonio2016-06-222016-06-222009Ariza Ruiz, D. y Jiménez Melado, A. (2009). A continuation method for weakly contractive mappings under the interior condition. Fixed Point Theory and Applications, 2009, 1-8.1687-1820http://hdl.handle.net/11441/42602Recently, 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1155/2009/809315