Relations between the generalized Bessel functions and the Janowski class

We are interested in finding the sufficient conditions on A, B, λ , b and c which ensure that the generalized Bessel functions uλ := uλ,b,c satisfies the subordination uλ (z) ≺ (1+ Az)/(1+ Bz). Also, conditions for which uλ (z) to be Janowski convex, and zu′ λ(z) to be Janowski starlike in the unit disk D = {z ∈C : |z| < 1} are obtained. Mathematics subject classification (2010): 34B30, 33C10, 30C80, 30C45.