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

By Miroslav Bacák, Simeon Reich. 2014

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We study a nonlinear semigroup associated with a nonexpansive mapping on an 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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/21ace0de265daf075f95aad8f4f49ab936499b26