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

Abstract

In this paper we apply proof mining techniques to compute, in the setting of 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.

minor corrections

References in corpus (2)

• Local stability of ergodic averages
• Proof mining in metric fixed point theory and ergodic theory