Relations between the generalized Bessel functions and the Janowski class

Abstract: We are interested in finding the sufficient conditions on $A$, $B$, $\lambda$, $b$ and $c$ which ensure that the generalized Bessel functions ${u}{\lambda}:={u}{\lambda,b,c}$ satisfies the subordination ${u}{\lambda}(z) \prec (1+Az)/ (1+Bz)$. Also, conditions for which ${u}{\lambda}(z)$ to be Janowski convex, and $z{u}'_{\lambda}(z)$ to be Janowski starlike in the unit disk $\mathbb{D}={z \in \mathbb{C}: |z|<1}$ are obtained.