A distortion theorem for the class of typically real functions

The author's investigations in the well known class $T$ of typically real functions $f(z)$ in the disk $U=\{z:|z|<1\}$ are prolonged. The region of values of the system $\{f(z_0),f(z_0),f(r_1),f(r_2),\dots,f(r_n)\}$ in the class $T$ is investigated. Here $z_0\in U$, $\operatorname{Im}z_0\ne0$, $0<r_j<1$ for $j=1,\dots,n$, $n\ge2$. As a corollary, the region of values of $f'(z_0)$ in the class of functions $f\in T$ with fixed values $f(z_0)$ and $f(r_j)$ $(j=1,\dots,n)$ is determined. In the proof a criterion of decision power moment problem is used. Bibl. – 10 titles.