Non–linear ergodic theorems in complete non–positive curvature metric spacesBulletin of Iranian Mathematical Society
Hadamard (or complete $CAT(0)$) spaces are complete, non–positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non–expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non–linear ergodic theorems for non–expansive maps on real Hilbert spaces, to non–expansive maps on Hadamard spaces, which include for example (possibly infinite dimensional) complete simply connected Riemannian manifolds with non–positive sectional curvature.
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