SUFFICIENT CONDITIONS FORSTARLIKENESS II

Abstract

In this paper we study a differential subordination of the form: azp'(z)+ap²(z)+(b-a)p(z)<h(z), where h(z)=anzq'(z)+aq²(z)+(b-a)q(z), with a>0, a+b>0, and the function q is convex with q(0)=1, and Req(z)>(a-b)/2a. Our results are obtained by using the method of differential subordinations developed in [1], [2] and [3]. For b=1, q(z)=1+lz and n=1 this problem was studied in [4].