The existence and non-existence of common fixed points for commuting families of holomorphic mappings
type: Item
instance of: scholarly article
title: The existence and non-existence of common fixed points for commuting families of holomorphic mappings
zbMATH Open document ID: 0968.47025
DOI: 10.1016/S0362-546X(99)00175-3
author: Tadeusz Kuczumow
author: Simeon Reich
author: David Shoikhet
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2000-12-03T00:00:00Z
review text: The main results of the paper are existence theorems for the common fixed points of commuting families of holomorphic or \(k_D\)-nonexpansive mappings on an open convex subset \(D\) of a Banach space. Also, the existence of stationary points and the behavior of the orbits for nonlinear semigroups of holomorphic mappings on the open unit ball of a Hilbert space are considered. An application to the following Cauchy problem: \[ \begin{cases} {\partial u(t,x)\over\partial t}+ u(t,x)- T(u(t, x))= 0\\ u(0,x)= x\end{cases} \] is also given.
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47J35
zbMATH DE Number: 1539290
zbMATH Keywords: common fixed points
zbMATH Keywords: commuting families of holomorphic or \(k_D\)-nonexpansive mappings
zbMATH Keywords: stationary points
zbMATH Keywords: nonlinear semigroups of holomorphic mappings
zbMATH Keywords: Cauchy problem
reviewed by: Adrian Petruşel
MaRDI profile type: Publication
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full work available at URL: s0362-546x(99)00175-3
OpenAlex ID: W2077699000
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