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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Strong pseudo-contractions perturbed by compact operators in Banach spaces


Author: Claudio H. Morales
Journal: Proc. Amer. Math. Soc. 133 (2005), 3613-3618
MSC (2000): Primary 47H10
DOI: https://doi.org/10.1090/S0002-9939-05-07942-6
Published electronically: June 7, 2005
MathSciNet review: 2163597
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Abstract: Let $X$ be a (real) Banach space, let $D$ be an open subset of $X$, and let $\mathcal{B}(X)$ denote the collection of all nonempty bounded and closed subsets of $X$. Suppose $T$ is continuous from $\overline{D}$ into $\mathcal{B}(X)$ with respect to the Hausdorff metric and strongly pseudo-contractive, while $g$ is compact from $\overline{D}$ into $X$. Then $T+g$ has a fixed point if it satisfies the classical Leray-Schauder condition on the boundary of $D$.


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Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-05-07942-6
Keywords: Strongly pseudo-contractive, pseudo-contractive, compact operators
Received by editor(s): December 3, 2003
Received by editor(s) in revised form: August 10, 2004
Published electronically: June 7, 2005
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2005 American Mathematical Society