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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Extreme points of classes of functions defined by subordination


Author: D. J. Hallenbeck
Journal: Proc. Amer. Math. Soc. 46 (1974), 59-64
MSC: Primary 30A32
DOI: https://doi.org/10.1090/S0002-9939-1974-0357757-2
MathSciNet review: 0357757
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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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DOI: https://doi.org/10.1090/S0002-9939-1974-0357757-2
Keywords: Starlike functions, convex functions, close-to-convex function, extreme point, probability measures, integral representation, subordination
Article copyright: © Copyright 1974 American Mathematical Society