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 (Formula Presented). We are interested in finding bounds on the growth of functions f and related issues, if there are known some properties of If 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 α-starlike functions as well as some interesting generalisations