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Transactions of the American Mathematical Society

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

 

 

Applications of extreme point theory to classes of multivalent functions


Authors: David J. Hallenbeck and Albert E. Livingston
Journal: Trans. Amer. Math. Soc. 221 (1976), 339-359
MSC: Primary 30A32
MathSciNet review: 0407257
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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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DOI: https://doi.org/10.1090/S0002-9947-1976-0407257-2
Keywords: Extreme point, closed convex hull, multivalent function, multivalent starlike function, multivalent convex function, multivalent close-to-convex function, majorization, subordination, $ {L^q}$ means
Article copyright: © Copyright 1976 American Mathematical Society