Applications of extreme point theory to classes of multivalent functions

Hallenbeck, David J.; Livingston, Albert E.

doi:10.1090/S0002-9947-1976-0407257-2

Applications of extreme point theory to classes of multivalent functions
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by David J. Hallenbeck and Albert E. Livingston PDF

Trans. Amer. Math. Soc. 221 (1976), 339-359 Request permission

Abstract:

Extreme points of the closed convex hulls of several classes of multivalent functions are determined. These are then used to determine the precise bounds on the coefficients of a function majorized by or subordinate to a function in any of the classes. ${L^q}$ means are also discussed and subordination theorems are considered. The classes we consider are generalizations of the univalent starlike, convex and close-to-convex functions in addition to others.

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