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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {On a~problem in the class of typically real functions},
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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/

[1] J. A. Jenkins, “Some problems for typically real functions”, Canad. J. Math., 13 (1961), 427–431 | DOI | MR

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

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

[4] M. G. Krein, A. A. Nudelman, Problema momentov Markova i ekstremalnye zadachi, M., 1973 | MR

[5] F. R. Gantmakher, Teoriya matrits, 5-e izd., M., 2010

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