Inclusion relations of q-Bessel functions associated with generalized conic domain

Abstract

In this paper, we investigate the geometric properties of Jackson and Hahn-Exton q-Bessel functions and perform their normalization for the analyticity in open unit disk E. By applying normalized Jackson and Hahn-Exton q-Bessel functions and idea of convolution we introduce a new operator and define new family of subclasses of analytic functions related with generalized conic domain. For these subclasses of analytic functions, we investigate inclusion relations and integral preserving properties. Also we will use q-Bernardi integral operator to discuss some applications of our main results.

Keywords

• analytic functions
• q-calculus
• q-derivative
• q-starlike functions
• q-convex functions
• q-bessel functions
• generalized conic domain ω^k，q