ESTIMATE OF $\[{d_0}/{d^'}\]$ FOR STARLIKE FUNCTIONS
Citation：
Huang Xinzhong.ESTIMATE OF $\[{d_0}/{d^'}\]$ FOR STARLIKE FUNCTIONS[J].Chinese Annals of Mathematics B,1986,7(2):139~146
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Authors：
Huang Xinzhong;
Abstract：
Let $\[{S^*}\]$ be the class of functions $\[f(t)\]$ analytic, univalent in the unit disk $\[\left| z \right| < 1\]$ and
map $\[\left| z \right| < 1\]$ onto a region which is starlike with respect to $\[w = 0\]$ and is denoted as $\[{D_f}\]$. Let
$\[{r_0} = {r_0}(f)\]$ be the radius of convexity of $\[f(2)\]$.
In this note, the author proves the following result:
$$\[\frac{{{d_0}}}{{{d^*}}} \ge 0.4101492\]$$
where $\[{d_0} = \mathop {\min }\limits_{\left| z \right| = {r_0}} f(z),{d^*} = \mathop {\inf }\limits_{\beta \in {D_f}} \left| \beta \right|\]$.
