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Effective results on nonlinear ergodic averages in \(\text{CAT}(\kappa)\) spaces. (English) Zbl 1362.37015

Summary: In this paper we apply proof mining techniques to compute, in the setting of \(\text{CAT}(\kappa)\) spaces (with \(\kappa>0\)), effective and highly uniform rates of asymptotic regularity and metastability for a nonlinear generalization of the ergodic averages, known as the Halpern iteration. In this way, we obtain a uniform quantitative version of a nonlinear extension of the classical von Neumann mean ergodic theorem.

MSC:

37A30 Ergodic theorems, spectral theory, Markov operators
47A35 Ergodic theory of linear operators
47H25 Nonlinear ergodic theorems
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