ON CERTAIN NEW CONDITIONS FOR STARLIKENESS AND STRONGLY-STARLIKENESS

Abstract

In this paper we will obtain conditions for starlikeness and strongly-starlikeness starting from the differential subordination of the form:

azp'(z)+p²(z)<h(z), where a³0, h(z)=anzq'(z)+q²(z), and q is a convex function in the unit disc U, with q(0)=1 and Req(z)>0, n³1. We will obtain our results by using the differential subordination method developed in [1], [2], [3].