ESTIMATE OF d_0/d~* FOR STARLIKE FUNCTIONS

Let S~* be the class of functionsf(z)analytic,univalent in the unit disk|z|<1 andmap|z|<1 onto a region which is starlike with respect to w=0 and is denoted as D_f.Letr_0=r_0(f)be the radius of convexity of f(2).In this note,the author proves the following result:(d_0/d~*)≥0.4101492,where d_0= f(z),d~*=|β|.

ESTIMATE OF $\[{d_0}/{d^'}\]$ FOR STARLIKE FUNCTIONS

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|\]$.