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The radius of starlikeness of certain analytic functions


Authors: P. L. Bajpai and Prem Singh
Journal: Proc. Amer. Math. Soc. 44 (1974), 395-402
MSC: Primary 30A32
DOI: https://doi.org/10.1090/S0002-9939-1974-0340578-4
MathSciNet review: 0340578
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Abstract: Let $ f(z) = \tfrac{1}{2}[zF(z)]'$, where $ F(z)$ is starlike of order $ \alpha ,0 \leqq \alpha < 1$ in $ D = \{ z:\vert z\vert < 1\} $. The purpose of this paper is to find out the disc in which $ f(z)$ is starlike of order $ \beta ,0 \leqq \beta < 1$. Results are best possible.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0340578-4
Keywords: Univalent functions, starlike functions of order $ \alpha $, radius of starlikeness
Article copyright: © Copyright 1974 American Mathematical Society

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