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Proceedings of the American Mathematical Society

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

 

 

Extreme points of subordination families with univalent majorants


Author: David J. Hallenbeck
Journal: Proc. Amer. Math. Soc. 91 (1984), 54-58
MSC: Primary 30C80; Secondary 30D55
MathSciNet review: 735563
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Abstract: Let $ s(F)$ denote the set of functions subordinate to a univalent function $ F$ in $ \Delta $ the unit disc. Let $ {B_0}$ denote the set of functions $ \phi (z)$ analytic in $ \Delta $ satisfying $ \phi (z)\left\vert { < 1} \right.$ and $ \phi (0) = 0$. We prove the following results: If $ f = F \circ \phi $ is an extreme point of $ s(F)$ and $ F(\Delta )$ is a Jordan domain, then $ \phi $ is an extreme point of $ {B_0}$.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0735563-0
Keywords: Analytic functions, bounded function, extreme point, Jordan domains, Nevanlinna class, subordinations, univalent function
Article copyright: © Copyright 1984 American Mathematical Society