Event № 146
In our previous work we used the notion of porosity to show that most of the nonexpansive self-mappings of bounded, closed and convex subsets of a Banach space are contractive and possess a unique fixed point, which is the uniform limit of all iterates. In this work we prove two variants of this result for nonexpansive self-mappings of closed and convex sets in a Banach space which are not necessarily bounded. As a matter of fact, it turns out that our results are true for all complete hyperbolic metric spaces. This is joint work with Alexander J. Zaslavski.