Strong pseudo-contractions perturbed by compact operators in Banach spaces
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- by Claudio H. Morales PDF
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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 $D$.References
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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
- 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
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 3613-3618
- MSC (2000): Primary 47H10
- DOI: https://doi.org/10.1090/S0002-9939-05-07942-6
- MathSciNet review: 2163597