Successive coefficients of convex functions

Abstract

It is shown that for $f$ analytic and convex in $z\in D=\{z:|z|<1\}$ and given by $f(z)=z+{\sum }_{n=2}^{\infty }{a}_n{z}^n$, the difference of coefficients $||a_3|-|a_2||\le 25/48$ and $||a_4|-|a_3||\le 25/48$ . Both inequalities are sharp.

Withdrawn by the author, since the results were found not to be best possible