On the difference of initial logarithmic coefficients for the class of univalent functions

In this paper we give estimates of the differences $\mathrm{\mid }{\gamma }_3\mathrm{\mid }-\mathrm{\mid }{\gamma }_2\mathrm{\mid }$ and $\mathrm{\mid }{\gamma }_4\mathrm{\mid }-\mathrm{\mid }{\gamma }_3\mathrm{\mid }$ for the class of functions $f$ univalent in the unit disc and normalized by $f(0)=f^{\mathrm{\prime }}(0)-1=0$. Here, ${\gamma }_2$, ${\gamma }_3$ and ${\gamma }_4$ are the initial logarithmic coefficients of the function $f$.