Certain Geometrical Properties and Hardy Space of Generalized k-Bessel Functions

In this paper, we study certain geometric properties such as the starlikeness of order ζ and the convexity of order ζ of the generalized k-Bessel function. In addition, we establish several requirements for the parameters so that the generalized k-Bessel function belongs to some subclasses of analytic functions. Furthermore, as an application of the geometric properties, we establish certain results concerning the Hardy spaces of the generalized k-Bessel function. On the other hand, we present some corollaries concerning the classical Bessel function Jρ and the modified Bessel function Iρ. To support our geometric results, we present some specific examples of functions that map the open unit disk onto the symmetric domains with respect to the real axis.