Bounds for radii of convexity of some $q$-Bessel functions
Bull. Korean Math. Soc. 2020 Vol. 57, No. 2, 355-369
Published online October 16, 2019
Printed March 31, 2020
Ibrahim Aktas, Halit Orhan
Karamano\u{g}lu Mehmetbey University; Atat\"{u}rk University
Abstract : 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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