A porosity theorem for a class of nonexpansive set-valued mappings
Simeon Reich, Alexander J. Zaslavski · Contemporary mathematics - American Mathematical Society · 2017
We consider a complete metric space ( M , d ) (\mathcal {M}, d) of nonexpansive set-valued self-mappings of a closed and convex (not necessarily bounded) set in a Banach space. We show that the subset of ( M , d ) (\mathcal {M}, d) which consists of those mappings which have approximate fixed points has a σ \sigma -porous complement in ( M , d ) (\mathcal {M}, d) .