Effective results on nonlinear ergodic averages in CAT$(κ)$ spaces

In this paper we apply proof mining techniques to compute, in the setting of CAT$(κ)$ spaces (with $κ>0$), 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.

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