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

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.