Sufficient conditions for Janowski starlike functions with fixed second coefficient

Let A, B, D, E∈ [- 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 + αzp^′(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 + αzp^′(z) / p(z) , αp²(z) + λzp^′(z) , αp(z) + (1 - α) p²(z) + λzp^′(z) , and (1 - α) p(z) + α(1 + zp^′(z) / p(z)). Also, sufficient conditions for Janowski starlikeness with fixed second coefficient are obtained.