Let T be the class of functions \( f(z)=z+\sum \limits_{n=2}^{\infty }{c}_n{z}^n \) regular and typically real in the disk |z| < 1. Sharp estimates for the coefficients c4 and c5 in terms of f′(r) are obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. S. Robertson, “On the coefficients of a typically-real function,” Bull. Amer. Math. Soc., 41, 565–572 (1935).
G. M. Goluzin, “On typically real functions,” Math. Sb., 27(69), No. 2, 201–218 (1950).
E. G. Goluzina, “On the mutual change of values of the derivative and third coefficient in a class of regular functions,” Zap. Nauchn. Semin. POMI, 453, 15–21 (2016).
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).
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to the memory of G. V. Kuzmina
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 463, 2017, pp. 36–43.
Translated by E. G. Goluzina.
Rights and permissions
About this article
Cite this article
Goluzina, E.G. On the Mutual Change of the Coefficients and Values of the Derivative in a Class of Regular Functions. J Math Sci 232, 768–773 (2018). https://doi.org/10.1007/s10958-018-3906-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-018-3906-x