Let $ C$ be a nonempty closed convex bounded subset of a Banach space $ E$. Let $ \mathcal{M}$ denote the family of all multivalued mappings from $ C$ into $ E$ which are nonempty weakly compact convex valued, $ \omega $-nonexpansive and weakly-weakly u.s.c., endowed with the metric of uniform convergence. Let $ {\mathcal{M}_0}$ be the set of all $ F \in \mathcal{M}$ for which the fixed point problem is well posed. It is proved that the set $ \mathcal{M}\backslash {\mathcal{M}_0}$ is $ \sigma $-porous (in particular meager). A similar result is given for weak properness.

On the porosity of the set of w-nonexpansive mappings without fixed points

Myjak, J.
;
Sampalmieri, R.
1992-01-01

Abstract

Let $ C$ be a nonempty closed convex bounded subset of a Banach space $ E$. Let $ \mathcal{M}$ denote the family of all multivalued mappings from $ C$ into $ E$ which are nonempty weakly compact convex valued, $ \omega $-nonexpansive and weakly-weakly u.s.c., endowed with the metric of uniform convergence. Let $ {\mathcal{M}_0}$ be the set of all $ F \in \mathcal{M}$ for which the fixed point problem is well posed. It is proved that the set $ \mathcal{M}\backslash {\mathcal{M}_0}$ is $ \sigma $-porous (in particular meager). A similar result is given for weak properness.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/120861
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