English

Relations between the generalized Bessel functions and the Janowski class

Complex Variables 2016-07-08 v1

Abstract

We are interested in finding the sufficient conditions on AA, BB, λ\lambda, bb and cc which ensure that the generalized Bessel functions uλ:=uλ,b,c{u}_{\lambda}:={u}_{\lambda,b,c} satisfies the subordination uλ(z)(1+Az)/(1+Bz){u}_{\lambda}(z) \prec (1+Az)/ (1+Bz). Also, conditions for which uλ(z){u}_{\lambda}(z) to be Janowski convex, and zuλ(z)z{u}'_{\lambda}(z) to be Janowski starlike in the unit disk D={zC:z<1}\mathbb{D}=\{z \in \mathbb{C}: |z|<1\} are obtained.

Keywords

Cite

@article{arxiv.1607.02100,
  title  = {Relations between the generalized Bessel functions and the Janowski class},
  author = {S. Kanas and S. R. Mondal and A. D. Mohammed},
  journal= {arXiv preprint arXiv:1607.02100},
  year   = {2016}
}
R2 v1 2026-06-22T14:48:29.584Z