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 ${u}_λ:={u}_{λ,b,c}$ satisfies the subordination ${u}_λ(z) \prec (1+Az)/ (1+Bz)$. Also, conditions for which ${u}_λ(z)$ to be Janowski convex, and $z{u}'_λ(z)$ to be Janowski starlike in the unit disk $\mathbb{D}=\{z \in \mathbb{C}: |z|<1\}$ are obtained.

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