NOTE ON SOME CLASSES OF HOLOMORPHIC FUNCTIONS RELATED TO JACK'S AND SCHWARZ'S LEMMA

Abstract

In this paper we discuss holomorphic mappings f of the unit disc U and corresponding index defined as I-f (z) = zf'(z)/f(z). We are interested in finding f(z) bounds on the growth of functions f and related issues, if there are known some properties of I-f on U. Our main tool in accomplishing this connection is Jack's lemma As a special case, we got estimates on the growth of some classes of alpha-starlike functions as well as some interesting generalisations.