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

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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. 
@article{ZNSL_2013_419_a3,
     author = {E. G. Goluzina},
     title = {On a~problem in the class of typically real functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {43--51},
     publisher = {mathdoc},
     volume = {419},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_419_a3/}
}
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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/