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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The univalence of an integral


Author: W. M. Causey
Journal: Proc. Amer. Math. Soc. 27 (1971), 500-502
MSC: Primary 30.42
MathSciNet review: 0280700
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Abstract: Let $ f(z)$ be a normalized function, analytic and univalent in the open unit disc. It is shown that if $ g(z) = \int_0^z {{{(f(t)/t)}^\alpha }dt} $, then $ g$ is univalent in the open unit disc if $ \alpha $ is a complex number satisfying $ 0 \leqq \vert\alpha \vert \leqq (\surd 2 - 1)/4$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0280700-9
PII: S 0002-9939(1971)0280700-9
Keywords: Schwarzian derivative, Poisson integral, univalent functions
Article copyright: © Copyright 1971 American Mathematical Society