Theorems of Wolff–Denjoy type for semigroups of nonexpansive mappings in geodesic spaces

Abstract

We show that if is a one‐parameter continuous semigroup of nonexpansive mappings acting on a complete locally compact geodesic space that satisfies some geometric properties, then there exists such that S converge uniformly on bounded sets of Y to ξ. In particular, our result applies to strictly convex bounded domains in or with respect to a large class of metrics including Hilbert's and Kobayashi's metrics.