Two porosity theorems for nonexpansive mappings in hyperbolic spaces (Q499201)

In the previous paper [C. R. Acad. Sci., Paris, Sér. I, Math. 333, No. 6, 539--544 (2001; Zbl 1001.47036)] the authors showed that most of the nonexpansive self-maps, in the sense of \(\sigma\)-porosity, defined on bounded, closed and convex subsets of a Banach space, are contractive. In the present paper, they show that a version of this result is valid also for unbounded sets and, moreover, the same is true in a hyperbolic metric space.