Affiliation:
1. Department of Mathematics, Faculty of Education, Ağrı İbrahim Çeçen University , Ağrı , Turkey
Abstract
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.
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