Growth Estimates of Convex Functions

Abstract

In this paper we generalize a result of Loewner's by use of an iterated form of the Schwarz Lemma.This tool is used repeatedly to obtain several results on the growth of convex analytic functions. Preliminaries.By a convex function we will mean a univalent analytic function, defined on the unit disc, whose range is a convex point set.Such a function/ satisfies the differential inequality: