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

Abstract

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