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Proceedings of the American Mathematical Society

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On a theorem of Duren, Shapiro and Shields


Author: Shinji Yamashita
Journal: Proc. Amer. Math. Soc. 73 (1979), 180-182
MSC: Primary 30C55
DOI: https://doi.org/10.1090/S0002-9939-1979-0516460-0
MathSciNet review: 516460
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Abstract: We shall show that, an extension of the theorem of Duren, Shapiro and Shields on the univalence of a function f holomorphic in the unit disk D, still remains of significance, if the power $ \alpha \in (0,1)$ in

$\displaystyle {\sup _{z \in D}}{(1 - \vert z{\vert^2})^\alpha }\vert f''(z)/f'(z)\vert$

is small enough.

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DOI: https://doi.org/10.1090/S0002-9939-1979-0516460-0
Article copyright: © Copyright 1979 American Mathematical Society