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If we have $k(z)=\frac{z}{1-tz}$ which is convex in unit disk, then $k(\bar{z})=\overline{k(z)}$, $k(z)$ maps real axis to real axis where $|z|\leq{r}$, $t\in\mathbb{R}$. What is the upper and lower bounds of $\Re {k(z)}$?

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    If $r\ge1/t$ then there can't be any upper bound since $k\to\infty$ as $z\to1/t$2011-12-02

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