Inclusion of generalized Bessel functions in the Janowski class

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 $u_{p,b,c}(z)\prec (1+Az)\mathrm{/}(1+Bz)$. In particular this gives conditions for $(-4\kappa \mathrm{/}c)(u_{p,b,c}(z)-1)$, $c\mathrm{\ne }0$ 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 $\mathbb{D}=\{z\in \mathbb{C}:\mathrm{\mid }z\mathrm{\mid }<1\}$ are obtained.