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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fixed points of univalent functions II


Author: Gerald Schmieder
Journal: Proc. Amer. Math. Soc. 134 (2006), 3605-3611
MSC (2000): Primary 30C35, 30D40
Published electronically: June 9, 2006
MathSciNet review: 2240673
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Abstract: For a closed nowhere dense subset $ C$ of $ \partial\mathbb{D}$ a bounded univalent holomorphic function $ f$ on $ \mathbb{D}$ is found such that $ C$ equals the cluster set of its fixed points.


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Additional Information

Gerald Schmieder
Affiliation: Fakultät V, Institut für Mathematik, Universität Oldenburg, D-26111 Oldenburg, Germany

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08442-5
PII: S 0002-9939(06)08442-5
Keywords: Univalent functions, fixed points, cluster set
Received by editor(s): December 14, 2004
Received by editor(s) in revised form: June 30, 2005
Published electronically: June 9, 2006
Dedicated: To my friend Masakazu Shiba on the occasion of his 60th birthday
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.