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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the extreme points of some sets of analytic functions
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by John G. Milcetich
Proc. Amer. Math. Soc. 45 (1974), 223-228
DOI: https://doi.org/10.1090/S0002-9939-1974-0352470-X

Abstract:

Let $A$ denote the set of analytic functions defined on the open unit disc. The extreme points of $F = \{ f \epsilon A:f(0) = 0$ and $|\operatorname {Re} f(z)| < \pi /2$ are determined. Also a partial characterization is given for the extreme points of ${G_\alpha } = \{ f\epsilon A:f(0) = 1$ and $|\arg f(z)| < \alpha \pi /2\} ,0 < \alpha < 1$.
References
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Bibliographic Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 45 (1974), 223-228
  • MSC: Primary 30A76
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0352470-X
  • MathSciNet review: 0352470