Fixed point theorems for metric spaces with a conical geodesic bicombing
Metric Geometry
2023-03-13 v1 Dynamical Systems
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.
Cite
@article{arxiv.1509.01691,
title = {Fixed point theorems for metric spaces with a conical geodesic bicombing},
author = {Giuliano Basso},
journal= {arXiv preprint arXiv:1509.01691},
year = {2023}
}
Comments
19 pages