Sufficient Conditions for Janowski Starlikeness

Let A,B,D,E ∈ [−1,1] and let p(z) be an analytic function defined on the open unit disk, p(0) = 1. Conditions on A, B, D, and E are determined so that 1 + βzp′(z) being subordinated to (1+Dz)/(1+Ez) implies that p(z) is subordinated to (1+Az)/(1+Bz). Similar results are obtained by considering the expressions 1 + β(zp′(z)/p(z)) and 1 + β(zp′(z)/p2(z)). These results are then applied to obtain sufficient conditions for analytic functions to be Janowski starlike.