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On some geometric results for generalized k-Bessel functions

Toklu Evrim

Demonstratio Mathematica

2023

Vol. 56, nr 1

art. no. 20220235

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