Geodesic
On the value region of $f(z_0)$ in one class of typically real functions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 14, Tome 237 (1997), pp. 46-55

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Let $T_R$ be the class of functions $f(z)$ with $f(0)=0$ and $f'(0)=1$ that are regular and typically real in the disk $|z|1$. The region of values of the system $\{f(z_0), f(r), f''(0)/2\}$ (for fixed $z_0$ and $r$, $0$) on the class $T_R$ is determined. The region of values of $f(z_0)$ on the class of functions from $T_R$ with fixed $f(r)$ and $f''(0)$ is found. 
@article{ZNSL_1997_237_a5,
     author = {E. G. Goluzina},
     title = {On the value region of $f(z_0)$ in one class of typically real functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {46--55},
     publisher = {mathdoc},
     volume = {237},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_237_a5/}
}
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E. G. Goluzina. On the value region of $f(z_0)$ in one class of typically real functions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 14, Tome 237 (1997), pp. 46-55. http://geodesic.mathdoc.fr/item/ZNSL_1997_237_a5/