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

#### 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.
##### Scheda breve Scheda completa Scheda completa (DC)
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/120861
• ND
• 2
• 2