Sufficient conditions for Janowski starlike functions with fixed second coefficient

Let A, B, D, E is an element of [-1, 1] and let p(z) be an analytic function with fixed initial coefficient defined in the open unit disk. Conditions on A, B, D, and E are determined so that 1+alpha zp' (z) being subordinated to (1+Dz)/(1+Ez) implies that p(z) is subordinated to (1+Az)/(1+Bz) and other similar implications involving 1 + alpha zp' (z) / p ( z), alpha p(2) (z) + lambda zp'(z), alpha p(z) + (1 - alpha)p(2)(z) + lambda zp'(z), and (1 - alpha)p(z) + alpha (1 + zp'(z)/p(z)). Also, sufficient conditions for Janowski starlikeness with fixed second coefficient are obtained.