Journal of Mathematical Sciences

, Volume 224, Issue 6, pp 821–825 | Cite as

On the Mutual Change of Values of the Derivative and Third Coefficient in a Class of Regular Functions

  • E. G. Goluzina

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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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia

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