Structure of the set of fixed points of uniformly Lipschitzian semigroups in CAT(0) spaces
Rafael Espı́nola, Aleksandra Huczek · Topological Methods in Nonlinear Analysis · 2025
Fixed points for semigroups of $k$-Lipschitz mappings have been recently studied under the considerations that the semigroup satisfies a mild amenability condition or that it is left reversible. Both approaches have brought positive results on existence of fixed points and structure of the set of fixed points. In the case of the amenable condition, results have been obtained for Hilbert spaces; in the case of left reversible semigroups, results were first obtained for Hilbert spaces and then extended to $p$-uniformly convex spaces. In this work, we address both approaches in the non linear context of complete CAT(0) spaces, providing counterparts of the most relevant results for each one of them.