On extreme points of subordination families

Author:
Yusuf Abu-Muhanna

Journal:
Proc. Amer. Math. Soc. **87** (1983), 439-443

MSC:
Primary 30C80

DOI:
https://doi.org/10.1090/S0002-9939-1983-0684634-5

MathSciNet review:
684634

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the set of analytic functions in subordinate to a univalent function . Let . For , let denote the distance between and (boundary of ). We obtain the following results.

(1) If is Nevanlinna then if and only if

(2) If is an extreme point of the closed convex hull of then

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0684634-5

Keywords:
Analytic function,
bounded function,
convex function,
extreme point,
Jordan domain,
Nevanlinna class,
subordination,
univalent function

Article copyright:
© Copyright 1983
American Mathematical Society