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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Extreme points of univalent functions with two fixed points


Author: Herb Silverman
Journal: Trans. Amer. Math. Soc. 219 (1976), 387-395
MSC: Primary 30A32
MathSciNet review: 0414853
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Abstract: Univalent functions of the form $ f(z) = {a_1}z - \Sigma _{n = 2}^\infty {a_n}{z^n}$, where $ {a_n} \geqslant 0$, are considered. We examine the subclasses for which $ f({z_0}) = {z_0}$ or $ f'({z_0}) = 1,{z_0}$ real. The extreme points of these classes that are starlike of order $ \alpha $ are determined.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0414853-5
PII: S 0002-9947(1976)0414853-5
Keywords: Univalent, starlike, convex, extreme point
Article copyright: © Copyright 1976 American Mathematical Society