A note on successive coefficients of convex functions

Abstract

In this note, we investigate the supremum and the infimum of the functional $|a_{n+1}|-|a_{n}|$ for functions, convex and analytic on the unit disk, of the form $f(z)=z+a_2z^2+a_3z^3+\dots.$ We also consider the related problem to maximize the functional $|a_{n+1}-a_{n}|$ for convex functions $f$ with $f"(0)=p$ for a prescribed $p\in[0,2].$