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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Extreme points for some classes of univalent functions

Authors: W. Hengartner and G. Schober
Journal: Trans. Amer. Math. Soc. 185 (1973), 265-270
MSC: Primary 30A36
MathSciNet review: 0335779
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Abstract: Monotonicity properties are given for extreme points in classes of normalized analytic and univalent mappings of an arbitrary domain. For the familiar class of normalized univalent mappings of the unit disk, extreme points f are shown to have the remarkable property that $ f/z$ is univalent.

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  • [1] L. Brickman, Extreme points of the set of univalent functions, Bull. Amer. Math. Soc. 76 (1970), 372-374. MR 41 #448. MR 0255788 (41:448)
  • [2] W. Hengartner and G. Schober, On schlicht mappings to domains convex in one direction, Comment. Math. Helv. 45 (1970), 303-314. MR 43 #3436. MR 0277703 (43:3436)
  • [3] T. Radó, Sur la représentation conforme des domaines variables, Acta. Sci. Math. (Szeged) 1 (1923), 180-186.

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Keywords: Univalent functions, extreme points
Article copyright: © Copyright 1973 American Mathematical Society

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