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Let C be a nonempty closed convex bounded subset of a Banach space E. Let X denote the family of all multivalued mappings from C into E which are nonempty weakly compact convex valued, co-nonexpansive and weakly-weakly u.s.c., endowed with the metric of uniform convergence. Let X0 be the set of all F E X4 for which the fixed point problem is well posed. It is proved that the set Yt\4'0 is a-porous (in particular meager). A similar result is given for weak properness.

On the porosity of the set of $\omega$-nonexpansive mappings without fixed points