Baire categories and classes of analytic functions in which the Wiman-Valiron type inequality can be almost surely improved

A. O. Kuryliak, O. B. Skaskiv, I. E. Chyzhykov

Let $f(z)={\sum }_{n=0}^{+\infty }{a}_n{z}^n$\ $(z\in \mathbb{C})$\ be an analytic function in the unit disk and $f_t$ be an analytic function of the form $f_t(z)=\sum_{n=0}^{+\infty} a_ne…