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Tangential limits of starlike univalent functions


Author: J. B. Twomey
Journal: Proc. Amer. Math. Soc. 97 (1986), 49-54
MSC: Primary 30C45; Secondary 30D40
DOI: https://doi.org/10.1090/S0002-9939-1986-0831385-2
MathSciNet review: 831385
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Abstract: Let $ f$ be starlike univalent in the unit disc, let $ \gamma > 1$ and let $ K > 0$. Then $ f(z)$ tends to a limit as $ z \to {e^{i\theta }}$ inside $ \{ z:\left\vert {{e^{i\theta }} - z} \right\vert \leq K{(1 - \left\vert z \right\vert)^{1/\gamma }}\} $ for every $ \theta $ in $ [0,2\pi ]$. This result is sharp.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0831385-2
Keywords: Tangential limits, univalent functions, starlike functions
Article copyright: © Copyright 1986 American Mathematical Society

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