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

 

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 | References | Similar Articles | Additional Information

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?)

  • 1. C. Caratheodory, Theory of functions of a complex variable. Vol. 2, Chelsea Publishing Company, New York, 1954. Translated by F. Steinhardt. MR 0064861 (16,346c)
  • 2. 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.
  • 3. Peter L. Duren, Univalent functions, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 259, Springer-Verlag, New York, 1983. MR 708494 (85j:30034)

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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
Email: A.F.Beardon@dpmms.cam.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03906-3
PII: S 0002-9939(97)03906-3
Keywords: Analytic, Schwarz-Pick, hyperbolic
Received by editor(s): May 1, 1996
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1997 American Mathematical Society