On some geometric properties and Hardy class of q-Bessel functions

In this paper, we deal with some geometric properties including starlikeness and convexity of order $\alpha$ of Jackson’s second and third $q$-Bessel functions which are natural extensions of classical Bessel function $J_{\nu }$. In additon, we determine some conditions on the parameters such that Jackson’s second and third $q$-Bessel functions belong to the Hardy space and to the class of bounded analytic functions.