Geodesic
On a problem in the class of typically real functions
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVI, Tome 419 (2013), pp. 43-51 
E. G. Goluzina. On a problem in the class of typically real functions. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVI, Tome 419 (2013), pp. 43-51. http://geodesic.mathdoc.fr/item/ZNSL_2013_419_a3/
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     author = {E. G. Goluzina},
     title = {On a~problem in the class of typically real functions},
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     year = {2013},
     volume = {419},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_419_a3/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $T$ be the class of functions $f(z)=z+\sum^\infty_{n=2}c_nz^n$ regular and typically real in the disk $U=\{z\in\mathbb C\colon|z|<1\}$. In the paper, sharp estimates on the derivative $f'(r)$ ($0) for functions in the class $T$ in terms of $f(r)$ and $c_2$ and also $f(r)$, $c_2$, and $c_3$ are obtained.

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