Leírás
In this talk we investigate zeros of monotone nonlinear operators in a Thompson metric space. Inspired by the work of Gaubert and Qu from 2014, we study exponentially contracting continuous and discrete time dynamical systems generated by these nonlinear operators. We establish the operator norm convergence of deterministic and stochastic resolvent and proximal type algorithms, in particular versions coming from a Trotter-Kato type formula. This generalizes strong law of large numbers and so called 'nodice' results proved for the Karcher mean of positive operators by Lim and Pálfia. Applications include generalization of these results from the Karcher mean to other, so called generalized Karcher means introduced in 2016 by Pálfia. We will discuss recent improvements on moment conditons under which these laws follow. The talk is based on recent joint works with Zoltán Léka.