Radii of <i>γ</i>-Spirallike of <i>q</i>-Special Functions

Abstract

The geometric properties of q-Bessel and q-Bessel-Struve functions are examined in this study. For each of them, three different normalizations are applied in such a way that the resulting functions are analytic in the unit disk of the complex plane. For these normalized functions, the radii of γ-spirallike and convex γ-spirallike of order σ are determined using their Hadamard factorization. These findings extend the known results for Bessel and Struve functions. The characterization of entire functions from the Laguerre-Pólya class plays an important role in our proofs. Additionally, the interlacing property of zeros of q-Bessel and q-Bessel-Struve functions and their derivatives is useful in the proof of our main theorems.

Keywords

• radii of γ-spirallike
• γ-spirallike functions
• q-Bessel functions
• q-Bessel-Struve functions