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

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.

Automated summary

This paper investigates the geometric properties of Jackson and Hahn-Exton q-Bessel functions and normalizes them for analyticity in the open unit disk E. By introducing a new operator using normalized q-Bessel functions and the concept of convolution, a new family of subclasses of analytic functions related to the generalized conic domain is defined. The inclusion relations and integral preserving properties of these subclasses of analytic functions are studied, and the q-Bernardi integral operator is used to discuss applications of the main results.