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 kk-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 kk-Bessel functions and some properties of real zeros of these functions.

Keywords

• k-bessel function
• univalent
• starlike and convex functions
• α-convex functions
• radius of uniform convexity
• radius of α-convexity
• 30c45
• 30d15
• 33c10