Geodesic
Estimating the second coefficient in the class of typically real functions with two function values prescribed
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXV, Tome 405 (2012), pp. 59-66

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Let $T_1$ be the class of functions $f(z)=z+c_2z^2+\cdots$ regular and typically real in the disk $|z|1$ whose values $f(r_1)$ and $f(z_2)$ are fixed, $0$. Let $T_2$ be the class of functions $f(z)=z+c_2z^2+\cdots$ regular and typically real in the disk $|z|1$ whose values $f(r_1)$ and $f(z_0)$ are fixed, $0$, $0|z_0|1$. Sharp estimates on the coefficient $c_2$ are obtained for the classes $T_1$ and $T_2$. 
@article{ZNSL_2012_405_a5,
     author = {E. G. Goluzina},
     title = {Estimating the second coefficient in the class of typically real functions with two function values prescribed},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {59--66},
     publisher = {mathdoc},
     volume = {405},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_405_a5/}
}
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E. G. Goluzina. Estimating the second coefficient in the class of typically real functions with two function values prescribed. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXV, Tome 405 (2012), pp. 59-66. http://geodesic.mathdoc.fr/item/ZNSL_2012_405_a5/