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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Schwarz-Pick Lemma for derivatives
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by A. F. Beardon PDF
Proc. Amer. Math. Soc. 125 (1997), 3255-3256 Request permission

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
  • Tadasi Nakayama, On Frobeniusean algebras. I, Ann. of Math. (2) 40 (1939), 611–633. MR 16, DOI 10.2307/1968946
  • 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
  • Email: A.F.Beardon@dpmms.cam.ac.uk
  • Received by editor(s): May 1, 1996
  • Communicated by: Theodore W. Gamelin
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 3255-3256
  • MSC (1991): Primary 30F45; Secondary 30C80
  • DOI: https://doi.org/10.1090/S0002-9939-97-03906-3
  • MathSciNet review: 1401727