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arXiv · 1509.01691

Fixed point theorems for metric spaces with a conical geodesic bicombing

Giuliano Basso
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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.

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Giuliano Basso. 2015-09-05. Fixed point theorems for metric spaces with a conical geodesic bicombing. https://doi.org/10.1017/etds.2016.106

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