On the Radius of Univalence and Starlikeness for Certain Analytic Functions

Throughout this paper we assume that

(1) f(z) = z+ a₂z² + is analytic for |z| < 1 and

(2) g(z) = z + b₂z² + is analytic and univalent for |z| < 1. Recently T. H. MacGregor [4] determined the radius of univalence of functionsf(z) satisfying |f(z)lg(z) - 1 | < 1, for | z | <1.