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Proceedings of the American Mathematical Society

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The Leray-Schauder condition for continuous pseudo-contractive mappings

Author: Claudio H. Morales
Journal: Proc. Amer. Math. Soc. 137 (2009), 1013-1020
MSC (2000): Primary 47H10; Secondary 65J15
Published electronically: September 24, 2008
MathSciNet review: 2457441
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Abstract: Over thirty years ago, Kirk raised the question of whether a nonexpansive mapping, defined on a convex domain with nonempty interior, has a fixed point under the Leray-Schauder condition, provided that its domain enjoys the Fixed Point Property with respect to nonexpansive self-mappings. In the present work we have found the answer to this question to be positive, even for a larger class of mappings. The result, indeed, represents a quite significant extension of a large number of theorems obtained in the last forty years. This also includes new theorems for nonexpansive mappings.

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Claudio H. Morales
Affiliation: Department of Mathematics, University of Alabama in Huntsville, Huntsville,Alabama 35899

Keywords: Pseudo-contractive operators, Leray-Schauder condition, and the fixed point property for nonexpansive self-mappings.
Received by editor(s): January 23, 2008
Received by editor(s) in revised form: March 12, 2008
Published electronically: September 24, 2008
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.