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Fixed point theorems for metric spaces with a conical geodesic bicombing



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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Fixed point theorems for metric spaces with a conical geodesic bicombing



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