Displaying similar documents to “On the Bohr radius for two classes of holomorphic functions.”

Averages of holomorphic mappings and holomorphic retractions on convex hyperbolic domains

Simeon Reich, David Shoikhet (1998)

Studia Mathematica

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Let D be a hyperbolic convex domain in a complex Banach space. Let the mapping F ∈ Hol(D,D) be bounded on each subset strictly inside D, and have a nonempty fixed point set ℱ in D. We consider several methods for constructing retractions onto ℱ under local assumptions of ergodic type. Furthermore, we study the asymptotic behavior of the Cesàro averages of one-parameter semigroups generated by holomorphic mappings.