On Bernardi's integral operator and the Briot–Bouquet differential subordination

Let A,B,D,E∈[−1,1]A,B,D,E∈[−1,1]. Conditions on A,B,DA,B,D and E are determined so thatp(z)+zp′(z)βp(z)+γ≺1+Dz1+Ezimpliesp(z)≺1+Az1+Bz. The result is applied to Bernardi's integral operator of two classes of analytic functions.