Bull. Korean Math. Soc. 2020; 57(2): 355-369
Online first article October 16, 2019 Printed March 31, 2020
https://doi.org/10.4134/BKMS.b190242
Copyright © The Korean Mathematical Society.
Ibrahim Aktas, Halit Orhan
Karamano\u{g}lu Mehmetbey University; Atat\"{u}rk University
In the present investigation, by applying two different normalizations of the Jackson's second and third $q$-Bessel functions tight lower and upper bounds for the radii of convexity of the same functions are obtained. In addition, it was shown that these radii obtained are solutions of some transcendental equations. The known Euler-Rayleigh inequalities are intensively used in the proof of main results. Also, the Laguerre-P\'olya class of real entire functions plays an important role in this work.
Keywords: Convex functions, radius of convexity, Mittag-Leffler expansions, $q$-Bessel functions, zeros of $q$-Bessel functions, Laguerre-P\'olya class of entire functions
MSC numbers: Primary 30C45, 30C15, 33C10
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