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
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