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

被引：0

作者：

Miroslav Bačák

Simeon Reich

机构：

[1] Max Planck Institute,Department of Mathematics

[2] The Technion – Israel Institute of Technology,undefined

来源：

Journal of Fixed Point Theory and Applications | 2014年 / 16卷

关键词：

Asymptotic behavior; Dirichlet problem; fixed point; heat flow; Hadamard space; nonlinear Markov operator; nonlinear semigroup; proximal point algorithm; resolvent; Primary 47H20; Secondary 47H09; 47H10; 47N10; 60J45;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：189 / 202

页数：13

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