Ergodic Methods for the Construction of Holomorphic Retractions
Let D be a bounded convex domain in a complex Banach space, and let F be a holomorphic self-mapping of D with a nonempty fixed point set. In this paper we study the flow generated by the mapping I — F on D, and use the asymptotic behavior of its Cesàro averages to construct a holomorphic retraction of D onto the fixed point set of F.
KeywordsNull Point Complex Banach Space Bounded Convex Domain Bounded Holomorphic Mapping Local Uniform Convergence
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