The application of the area principle to the Bieberbach–Eilenberg functions

A series of inequalities are obtained for the logarithmic areas of functions of the form $f(z)=\sum_{k=1}^\infty a_kz^k$ and $\varphi(z)=\frac{R}2+\sum_{k=0}^\infty a'_kz^k$, univalent in the circle $|z|<1$, and also for the Taylor coefficients of the Bieberbach–Eilenberg functions.