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 $f(z)=z+a_2{z}^2+a_3{z}^3+\dots .$ 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 $p\in [0,2].$

13 pages, 1 figure