Extreme points of subordination families with univalent majorants
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- by David J. Hallenbeck PDF
- Proc. Amer. Math. Soc. 91 (1984), 54-58 Request permission
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 $\phi (z)\left | { < 1} \right .$ 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 ${B_0}$.References
- Yusuf Abu-Muhanna, On extreme points of subordination families, Proc. Amer. Math. Soc. 87 (1983), no. 3, 439–443. MR 684634, DOI 10.1090/S0002-9939-1983-0684634-5
- Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
- Christian Pommerenke, Univalent functions, Studia Mathematica/Mathematische Lehrbücher, Band XXV, Vandenhoeck & Ruprecht, Göttingen, 1975. With a chapter on quadratic differentials by Gerd Jensen. MR 0507768
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 54-58
- MSC: Primary 30C80; Secondary 30D55
- DOI: https://doi.org/10.1090/S0002-9939-1984-0735563-0
- MathSciNet review: 735563