  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.
