The existence and non-existence of common fixed points for commuting families of holomorphic mappings (Q1588342)
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scientific article; zbMATH DE number 1539290
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The existence and non-existence of common fixed points for commuting families of holomorphic mappings |
scientific article; zbMATH DE number 1539290 |
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The existence and non-existence of common fixed points for commuting families of holomorphic mappings (English)
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3 December 2000
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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.
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common fixed points
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commuting families of holomorphic or \(k_D\)-nonexpansive mappings
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stationary points
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nonlinear semigroups of holomorphic mappings
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Cauchy problem
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0.9613547
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0.9550207
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0.94245124
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0.93243253
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0.9318155
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0.9208815
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