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Computational Methods and Function Theory

, Volume 3, Issue 1, pp 299–304 | Cite as

Fixed Points of Univalent Functions

  • Tatevik Gharibyan
  • Gerald Schmieder
Article
  • 42 Downloads

Abstract

We consider the class of univalent holomorphic functions f in the open unit disk. We prove that, if f is not the identity, the cluster set of the fixed points of f is a nowhere dense subset of the unit circle.

Keywords

Boundary behavior of univalent functions fixed points of univalent functions 

2000 MSC

30C55 30D40 

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References

  1. 1.
    E. F. Collingwood and A. J. Lohwater, The Theory of Cluster Sets, Cambridge University Press, Cambridge, 1966.MATHCrossRefGoogle Scholar
  2. 2.
    K. Doppel, H. Köditz and S. Timmann, Bemerkungen über Fixpunktmengen schlichter Funktionen, Rend. Ist. Mat. Univ. Trieste 8 (1976), 162–166.MathSciNetGoogle Scholar
  3. 3.
    M. Ohtsuka, Dirichlet Problem, Extremal Length and Prime Ends, Van Nostrand, London-Toronto-Melbourne, 1970.MATHGoogle Scholar
  4. 4.
    Ch. Pommerenke, Univalent Functions, Vandenhoeck & Ruprecht, Göttingen, 1975.MATHGoogle Scholar

Copyright information

© Heldermann  Verlag 2003

Authors and Affiliations

  1. 1.Department of MathematicsYerevan State UniversityYerevanRepublic of Armenia
  2. 2.Fakultät V, Institut für MathematikUniversität OldenburgOldenburgGermany

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