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Proceedings of the American Mathematical Society

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

 

 

A new proof for an inequality of Jenkins


Author: George B. Leeman
Journal: Proc. Amer. Math. Soc. 54 (1976), 114-116
DOI: https://doi.org/10.1090/S0002-9939-1976-0393457-2
MathSciNet review: 0393457
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Abstract | References | Additional Information

Abstract: A new proof of Jenkins' inequality

$\displaystyle \operatorname{Re} ({e^{2i\theta }}{a_3} - {e^{2i\theta }}a_2^2 - ... ... ^2} - \tfrac{1} {4}{\tau ^2}\log (\tau /4),\quad 0 \leqslant \tau \leqslant 4,$

for univalent functions $ f(z) = z + \sum\nolimits_{n = 2}^\infty {{a_n}{z^n}} $ is presented.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0393457-2
Keywords: Univalent functions, coefficient estimates
Article copyright: © Copyright 1976 American Mathematical Society