# Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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## Support points of families of analytic functions described by subordinationHTML articles powered by AMS MathViewer

by D. J. Hallenbeck and T. H. MacGregor
Trans. Amer. Math. Soc. 278 (1983), 523-546 Request permission

## Abstract:

We determine the set of support points for several families of functions analytic in the open unit disc and which are generally defined in terms of subordination. The families we study include the functions with a positive real part, the typically-real functions, and the functions which are subordinate to a given majorant. If the majorant $F$ is univalent then each support point has the form $F \circ \;\phi$, where $\phi$ is a finite Blaschke product and $\phi (0) = 0$. This completely characterizes the set of support points when $F$ is convex. The set of support points is found for some specific majorants, including $F(z) = {((1 + z)/(1 - z))^p}$ where $p > 1$. Let $K$ and ${\text {St}}$ denote the set of normalized convex and starlike mappings, respectively. We find the support points of the families ${K^{\ast } }$ and ${\text {St}}^{\ast }$ defined by the property of being subordinate to some member of $K$ or ${\text {St}}$, respectively.
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