On the mutual growth of neighboring coefficients of univalent functions

In the class $S$ of functions $f(z)=z+c_2z^2+c_3z^3+\dotsb$, regular and univalent in $|z|<1$, the following bound is obtained: $||c_{n+1}|-|c_n||<4.26$, $n=1,2,\dots$