  Let $\mathcal{S}$ denote the class of functions $f$ which are analytic and
univalent in the unit disk ${\mathbb D}=\{z:|z|<1\}$ and normalized with
$f(z)=z+\sum_{n=2}^{\infty} a_n z^n$. Using a method based on Grusky
coefficients we study two problems over the class $\mathcal{S}$: estimate of
the fourth logarithmic coefficient and upper bound of the coefficient
difference $|a_5|-|a_4|$.
