On some geometric results for generalized k-Bessel functions

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.

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Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).