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Fixed point theorems for metric spaces with a conical geodesic bicombing

Published online by Cambridge University Press:  14 February 2017

GIULIANO BASSO
GIULIANO BASSO*
Affiliation:
Mathematik Departement, ETH Zürich, Rämistrasse 101, 8092 Zürich, Schweiz email [email protected]
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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.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 5 , August 2018 , pp. 1642 - 1657
Copyright
© Cambridge University Press, 2017 

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