Let T be the class of functions \( f(z)=z+\sum_{n=2}^{\infty }{c}_n{z}^n \) regular and typically real in the disk |z| < 1. Sharp estimates for the derivative f ′(r)(0 < r < 1) in terms of the value c3 and sharp estimates for the coefficient c3 in terms of f′(r) are obtained.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 453, 2016, pp. 15–21.
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Goluzina, E.G. On the Mutual Change of Values of the Derivative and Third Coefficient in a Class of Regular Functions. J Math Sci 224, 821–825 (2017). https://doi.org/10.1007/s10958-017-3452-y
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DOI: https://doi.org/10.1007/s10958-017-3452-y