On some geometric results for generalized k-Bessel functions

Abstract The main aim of this article is to present some novel geometric properties for three distinct normalizations of the generalized k k -Bessel functions, such as the radii of uniform convexity and of α \alpha -convexity. In addition, we show that the radii of α \alpha -convexity remain in between the radii of starlikeness and convexity, in the case when α ∈ [ 0 , 1 ] , \alpha \in {[}0,1], and they are decreasing with respect to the parameter α . \alpha . The key tools in the proof of our main results are infinite product representations for normalized k k -Bessel functions and some properties of real zeros of these functions.