2019/02/24 by Evrim Toklu, Toklu, Evrim
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1902.09979
openalex publication_date 2019/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main purpose of this paper is to determine the radii of starlikeness and convexity of the generalized k-Bessel functions for three different kinds of normalization by using their Hadamard factorization in such a way that the resulting functions are analytic in the unit disk of the complex plane. The characterization of entire functions from Laguerre-Pólya class plays an crucial role in this paper. Moreover, the interlacing properties of the zeros of k-Bessel function and its derivative is also useful in the proof of the main results. By making use of the Euler-Rayleigh inequalities for the real zeros of the generalized k-Bessel function, we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero.