Briot-bouquet differential equations and differential subordinations

Abstract

Let β and γ be complex numbersn a positive integer, and let h be analytic in the unit disk U. This article describes conditions under which the Briot-Bouquet differential equation has analytic and univalent solutions. If h is also univalent then conditions are determined for the best dominants of the Briot-Bouquet differential subordination In addition, other differential subordinations are considered, together with applications to integral operators and to univalent functions.