Geodesic
On the mutual change of the coefficients and values of the derivative in a class of regular functions
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXX, Tome 463 (2017), pp. 36-43 
E. G. Goluzina. On the mutual change of the coefficients and values of the derivative in a class of regular functions. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXX, Tome 463 (2017), pp. 36-43. http://geodesic.mathdoc.fr/item/ZNSL_2017_463_a3/
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     author = {E. G. Goluzina},
     title = {On the mutual change of the coefficients and values of the derivative in a~class of regular functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {36--43},
     year = {2017},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_463_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 $|z|<1$. Sharp estimates for the coefficients $c_4$ and $c_5$ in terms of $f'(r)$ are obtained.

[1] M. S. Robertson, “On the coefficients of a typically-real function”, Bull. Amer. Math. Soc., 41 (1935), 565–572 | DOI | MR | Zbl

[2] G. M. Goluzin, “O tipichno veschestvennykh funktsiyakh”, Mat. sb., 27(69) (1950), 201–218 | MR | Zbl

[3] E. G. Goluzina, “O vzaimnom izmenenii proizvodnoi i tretego koeffitsienta v odnom klasse regulyarnykh funktsii”, Zap. nauchn. semin. POMI, 453, 2016, 15–21 | MR

[4] Yu. E. Alenitsyn, “Ob oblastyakh izmeneniya sistem koeffitsientov funktsii, predstavimykh summoi integralov Stiltesa”, Vestn. LGU, 1962, no. 7, Ser. mat., mekh. i astr., vyp. 2, 25–41 | Zbl