Inclusion of generalized Bessel functions in the Janowski class (1506.03138v1)

Abstract: 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.