Let T be the class of functions \( f(z)=z+{\displaystyle \sum_{n=r}^{\infty }{c}_n{z}^n} \) regular and typically real in the disk |z| < 1. Sharp estimates for the coefficients c 3 and c 4 in terms of the values f(r), 0 < r < 1, are obtained. Bibliography: 4 titles.
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M. S. Robertson, “On the coefficients of a typically-real function,” Bull. Amer. Math. Soc., 41, No. 8, 565–572 (1935).
G. M. Goluzin, “On typically real functions,” Mat. Sb., 27 (69) No. 2, 201–218 (1950).
Yu. E. Alenitsyn, “On the ranges of systems of coefficients of functions representable by a sum of Stieltjes integrals,” Vestn. Leningr. Gos. Univ., Ser. Mat., Mekh., Astr., Vyp. 2, No. 7, 25–41 (1962).
J. A. Jenkins, “Some problems for typically real functions,” Canad. J. Math., 13, No. 2, 427–431 (1961).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 428, 2014, pp. 81–88.
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Goluzina, E.G. Some Sharp Estimates for Typically Real Functions. J Math Sci 207, 718–723 (2015). https://doi.org/10.1007/s10958-015-2394-5
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DOI: https://doi.org/10.1007/s10958-015-2394-5