Tangential limits of starlike univalent functions

Twomey, J. B.

doi:10.1090/S0002-9939-1986-0831385-2

Tangential limits of starlike univalent functions
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by J. B. Twomey PDF

Proc. Amer. Math. Soc. 97 (1986), 49-54 Request permission

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 $\{ z:\left | {{e^{i\theta }} - z} \right | \leq K{(1 - \left | z \right |)^{1/\gamma }}\}$ for every $\theta$ in $[0,2\pi ]$. This result is sharp.

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