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arXiv · 1607.02100

Relations between the generalized Bessel functions and the Janowski class

S. Kanas·S. R. Mondal·A. D. Mohammed
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Abstract

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.

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S. Kanas, S. R. Mondal, A. D. Mohammed. 2016-07-07. Relations between the generalized Bessel functions and the Janowski class. https://arxiv.org/abs/1607.02100

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