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

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• 作者：Miroslav Ba?ák ; Simeon Reich
• 关键词：Primary 47H20 ; Secondary 47H09 ; 47H10 ; 47N10 ; 60J45 ; Asymptotic behavior ; Dirichlet problem ; fixed point ; heat flow ; Hadamard space ; nonlinear Markov operator ; nonlinear semigroup ; proximal point algorithm ; resolvent
• 刊名：Journal of Fixed Point Theory and Applications
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：16
• 期：1-2
• 页码：189-202
• 全文大小：601 KB
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• 作者单位：Miroslav Ba?ák (1)
  Simeon Reich (2)
  
  1. Max Planck Institute, Inselstr. 22, 04103, Leipzig, Germany
  2. Department of Mathematics, The Technion -Israel Institute of Technology, 32000, Haifa, Israel
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Mathematical Methods in Physics
  
• 出版者：Birkh盲user Basel
• ISSN：1661-7746

文摘

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.