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The Schwarz-Pick Lemma for derivatives

Author: A. F. Beardon
Journal: Proc. Amer. Math. Soc. 125 (1997), 3255-3256
MSC (1991): Primary 30F45; Secondary 30C80
MathSciNet review: 1401727
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Abstract: The Schwarz-Pick Lemma states that any analytic function of the unit disc into itself is a contraction with respect to the hyperbolic metric. In this note a related result is proved for the derivative of an analytic function.

References [Enhancements On Off] (What's this?)

  • C. Caratheodory, Theory of functions of a complex variable, Vol. II, Chelsea, 1960.
  • J. Dieudonne, Recherches sur quelques problemes relatifs aux polynomes et aux fonctions bornees d’une variable complexe, Ann. Sci. Ecole Norm. Sup. 48 (1931), 247–358.
  • Peter L. Duren, Univalent functions, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 259, Springer-Verlag, New York, 1983. MR 708494

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Additional Information

A. F. Beardon
Affiliation: Department of Pure Mathematics & Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB, England

Keywords: Analytic, Schwarz-Pick, hyperbolic
Received by editor(s): May 1, 1996
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1997 American Mathematical Society