Disk of univalence of the ratio of two analytic functions

Abstract

Let A denote the family of all functions f analytic in the unit disk D with the normalizationIn this paper, we determine the radius of univalency of F(z) = z f (z)/g(z), where f and g are chosen appropriately from S, U and P(1/2). The method used is different from the one used earlier and the present results improve the earlier known results.