Extreme points of univalent functions with two fixed points

Silverman, Herb

doi:10.1090/S0002-9947-1976-0414853-5

Extreme points of univalent functions with two fixed points
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Trans. Amer. Math. Soc. 219 (1976), 387-395 Request permission

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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