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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.

Bounds for radii of convexity of some $q$-Bessel functions

Ibrahim Aktas, Halit Orhan

Karamano\u{g}lu Mehmetbey University; Atat\"{u}rk University

Abstract

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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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