Extreme points of classes of functions defined by subordination

Hallenbeck, D. J.

doi:10.1090/S0002-9939-1974-0357757-2

Extreme points of classes of functions defined by subordination
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Proc. Amer. Math. Soc. 46 (1974), 59-64 Request permission

Abstract:

The closed convex hull and extreme points of families of analytic functions, which are defined in terms of subordination, are determined. Integral representations are given for the hulls of these families in terms of probability measures on suitable sets. These results are used to solve extremal problems. The functions we consider are defined by subordination to certain classes of starlike and convex mappings.

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