Univalent solutions of Briot-Bouquet differential equations

Abstract

Let β and γ be complex numbers and let h(z) be regular in the unit disc U. In this article the authors study the Briot-Bouquet differential equation

$$q(z) + \frac{{zq'(z)}}{{\beta q(z) + \gamma }} = h(z).$$

Sufficient conditions are obtained for both the regularity and univalency of the solution in U. In addition, applications of these results to differential subordinations, integral operators and univalent functions are given.

This work was carried out while this author was a U.S.A.-Romanian Exchange Scholar.