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Proceedings of the American Mathematical Society

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

 

 

A Loewner approach to a coefficient inequality for bounded univalent functions


Authors: Duane W. De Temple and James A. Jenkins
Journal: Proc. Amer. Math. Soc. 65 (1977), 125-126
MSC: Primary 30A34
DOI: https://doi.org/10.1090/S0002-9939-1977-0444932-4
MathSciNet review: 0444932
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Abstract: The Loewner theory is used to obtain the sharp upper bound for the functional $ \operatorname{Re} \{ {e^{2i\theta }}({a_3} - a_2^2) + 4\sigma {e^{i\theta }}{a_2}\} $ over the class of univalent functions $ f(z) = b(z + {a_2}{z^2} + {a_3}{z^3} + \ldots )$ which map the unit disc into itself; $ \theta \in {\mathbf{R}},\sigma \in [0,1]$ and $ b \in (0,1]$ are fixed parameters.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0444932-4
Keywords: Univalent functions, bounded univalent functions
Article copyright: © Copyright 1977 American Mathematical Society