Proceedings of the American Mathematical Society

Author(s): Claudio H. Morales
Journal: Proc. Amer. Math. Soc. 137 (2009), 1013-1020.
MSC (2000): Primary 47H10; Secondary 65J15
Posted: September 24, 2008
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47H10, 65J15

Claudio H. Morales
Affiliation: Department of Mathematics, University of Alabama in Huntsville, Huntsville, Alabama 35899
Email: morales@math.uah.edu

DOI: 10.1090/S0002-9939-08-09570-1
PII: S 0002-9939(08)09570-1
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
Posted: September 24, 2008
Communicated by: Nigel J. Kalton
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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