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Proceedings of the American Mathematical Society

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

 

 

A further refinement for coefficient estimates of univalent functions


Author: David Horowitz
Journal: Proc. Amer. Math. Soc. 71 (1978), 217-221
MSC: Primary 30A34
DOI: https://doi.org/10.1090/S0002-9939-1978-0480979-0
MathSciNet review: 0480979
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Abstract: The coefficient inequalities of FitzGerald are used to show that if $ f(z) = z + {a_2}{z^2} + {a_3}{z^3} + \ldots $ is analytic and univalent in the unit disc, then $ \vert{a_n}\vert < (1.0657)n$. The technique used to obtain this bound cannot yield a result better than $ \vert{a_n}\vert < (1.0599)n$.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0480979-0
Article copyright: © Copyright 1978 American Mathematical Society