Fixed point theorems for metric spaces with a conical geodesic bicombing

Abstract

We derive two fixed point theorems for a class of metric spaces that includes all Banach spaces and all complete Busemann spaces. We obtain our results by the use of a 1-Lipschitz barycenter construction and an existence result for invariant Radon probability measures. Furthermore, we construct a bounded complete Busemann space that admits an isometry without fixed points.

19 pages

References in corpus (1)

• Nonexpansive iterations in uniformly convex $W$-hyperbolic spaces

Cited by in corpus (2)

• Conical geodesic bicombings on subsets of normed vector spaces
• Lipschitz extension theorems with explicit constants