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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
55/2014

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

Miroslav Bačák and Simeon Reich

Abstract

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.

Received:
May 28, 2014
Published:
May 28, 2014
MSC Codes:
47H20, 60J45
Keywords:
dirichlet problem, fixed point, Hadamard space, heat flow, nonlinear Markov operator, proximal point algorithm, resolvent, semigroup

Related publications

inJournal
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