Strong Differential Subordination to Briot-Bouquet Differential Equations

Let p(z) be analytic in the unit disc D, let g(z) be convex in D, let ƒ(z) be analytic in D such that z(ƒ′(z)/ƒ(z)) is analytic and different from zero in D, and let α and β be complex numbers. The authors show that if [formula], where denotes subordination and [formula] is satisfied, then p(z) g(z). Further, if the differential equation [formula] verifying (1), has a univalent solution q(z), then sharp subordination p(z) q(z) holds.