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The Schwarz-Pick Lemma for derivatives

Author(s): A. F. Beardon
Journal: Proc. Amer. Math. Soc. 125 (1997), 3255-3256.
MSC (1991): Primary 30F45; Secondary 30C80
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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:

1.: C. Caratheodory, Theory of functions of a complex variable, Vol. II, Chelsea, 1960. MR 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.: P. L. Duren, Univalent functions, Springer-Verlag, 1983. MR 85j:30034


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