Geodesic
A distortion theorem for the class of typically real functions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 23, Tome 357 (2008), pp. 33-45 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 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. 
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E. G. Goluzina. A distortion theorem for the class of typically real functions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 23, Tome 357 (2008), pp. 33-45. http://geodesic.mathdoc.fr/item/ZNSL_2008_357_a2/

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