Event № 170
In my previous talk (which is not a prerequisite for this one) we have seen that the set of strict contractions on a bounded, closed and convex subset of a Banach space is a small subset of the space of all nonexpansive mappings. In this talk we show that the set of strict contractions on $\rho$-convex or more generally, $\rho$-star-shaped subsets of certain metric spaces $(X,\rho)$ is small in the sense that it is a $\sigma$-porous subset of the space of nonexpansive mappings. The class of metric spaces for which we can prove this result contains the class of hyperbolic spaces. This is joint work with Michael Dymond and Simeon Reich.