The existence and non-existence of common fixed points for commuting families of holomorphic mappings
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.
commuting families of holomorphic or \(k_D\)-nonexpansive mappings
nonlinear semigroups of holomorphic mappings
scientific article; zbMATH DE number 1539290
scientific article