Effective results on nonlinear ergodic averages in CAT...spaces

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