On some geometric properties and Hardy class of q-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 Jν. 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.

Keywords

• analytic function
• convex and starlike functions of order α
• hardy space
• q-bessel functions