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Effective results on nonlinear ergodic averages in CAT $(\unicode[STIX]{x1D705})$ spaces

  • LAURENŢIU LEUŞTEAN (a1) (a2) and ADRIANA NICOLAE (a3) (a4)

In this paper we apply proof mining techniques to compute, in the setting of CAT $(\unicode[STIX]{x1D705})$ spaces (with $\unicode[STIX]{x1D705}>0$ ), 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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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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