On some geometric properties and Hardy class of <i>q</i>-Bessel functions

Abstract

In this paper, we deal with some geometric properties including starlikeness and convexity of order α of Jackson's second and third q-Bessel functions which are natural extensions of classical Bessel function J ν . 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.where z ∈ C, ν > −1, q ∈ (0, 1) and (a; q) 0 = 1, (a; q) n = n k=1 1 − aq k−1 , (a, q) ∞ = k≥1 1 − aq k−1 .