  Sufficient conditions on $A$, $B$, $p$, $b$ and $c$ are determined that will
ensure the generalized Bessel functions ${u}_{p,b,c}$ satisfies the
subordination ${u}_{p,b,c}(z) \prec (1+Az)/ (1+Bz)$. In particular this gives
conditions for $(-4\kappa/c)({u}_{p,b,c}(z)-1)$, $c \neq 0$ to be
close-to-convex. Also, conditions for which ${u}_{p,b,c}(z)$ to be Janowski
convex, and $z{u}_{p,b,c}(z)$ to be Janowski starlike in the unit disk
$\mathbb{D}=\{z \in \mathbb{C}: |z|<1\}$ are obtained.
