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MiS Preprint

The asymptotic behavior of a class of nonlinear semigroups in Hadamard spaces

Miroslav Bačák and Simeon Reich


We study a nonlinear semigroup associated to a nonexpansive mapping on a Hadamard space and establish its weak convergence to a fixed point. A discrete-time counterpart of such a semigroup, the proximal point algorithm, turns out to have the same asymptotic behavior. This complements several results in the literature – both classical and more recent ones. As an application, we obtain a new approach to heat flows in singular spaces for discrete, as well as continuous times.

MSC Codes:
47H20, 60J45
dirichlet problem, fixed point, Hadamard space, heat flow, nonlinear Markov operator, proximal point algorithm, resolvent, semigroup

Related publications

2014 Repository Open Access
Miroslav Bačák and Simeon. Reich

The asymptotic behavior of a class of nonlinear semigroups in Hadamard spaces

In: Journal of fixed point theory and applications, 16 (2014) 1-2, pp. 189-202