Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

The Leray-Schauder condition for continuous pseudo-contractive mappings

Author(s): Claudio H. Morales
Journal: Proc. Amer. Math. Soc. 137 (2009), 1013-1020.
MSC (2000): Primary 47H10; Secondary 65J15
Posted: September 24, 2008
MathSciNet review: 2457441
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Abstract | References | Similar articles | Additional information

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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