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Fixed points of univalent functions II
Author:
Gerald Schmieder
Journal:
Proc. Amer. Math. Soc. 134 (2006), 3605-3611
MSC (2000):
Primary 30C35, 30D40
Posted:
June 9, 2006
MathSciNet review:
2240673
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Abstract: For a closed nowhere dense subset  of  a bounded univalent holomorphic function  on  is found such that  equals the cluster set of its fixed points.
References
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Collingwood, E.F., Lohwater, A.J.: The theory of cluster sets. Cambridge University Press, Cambridge 1966. MR 0231999 (38:325)
- 2.
Doppel, K., Köditz, H., Timmann, S.: Bemerkungen über Fixpunktmengen schlichter Funktionen. Rend. Ist. di Matem. Univ. di Trieste vol. VII, fasc. II (1976), 161-165. MR 0463424 (57:3375)
- 3.
Gaier, D.: Lectures on complex approximation (translated from the german). Birkhäuser, Boston-Basel-Stuttgart 1987. MR 0894920 (88i:30059b)
- 4.
Gharibyan, T., Schmieder, G.: Fixed Points of Univalent Funktions. Computational Methods and Function Theory 3 (2003), 299-304. MR 2082019 (2005d:30049)
- 5.
Ohtsuka, M.: Dirichlet problem, extremal length and prime ends. Van Nostrand, London-Toronto-Melbourne 1970.
- 6.
Pommerenke, C.: Univalent functions. Vandenhoeck & Ruprecht, Göttingen 1975. MR 0507768 (58:22526)
- 7.
Schmieder, G.: Fusion lemma and boundary structure. J. Approx. Theory 71 (1992), 305-311. MR 1191577 (94a:30032)
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Schmieder, G., Shiba, M.: Über ein Lemma der komplexen Approximationstheorie. Manuscripta Math. 65 (1989), 447-464. MR 1019702 (90j:30064)
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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
Posted:
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 after
28 years from publication.
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