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ArticleOriginal scientific text

Title

Averages of holomorphic mappings and holomorphic retractions on convex hyperbolic domains

Authors 1, 2

Affiliations

  1. Department of Mathematics, The Technion-Israel Institute of Technology, 32000 Haifa, Israel
  2. Department of Applied Mathematics, International College of Technology, P.O. Box 78, 20101 Karmiel, Israel

Abstract

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.

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Studia Mathematica
1998/130/3
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Pages:
231-244
Main language of publication
English
Received
1997-08-20
Accepted
1998-02-20
Published
1998
Exact and natural sciences