Radii of starlikeness and convexity of Bessel function  derivatives

E.  Deniz; S.  Kazımoğlu; M. Çağlar

doi:10.37863/umzh.v73i11.1014

E. Deniz Kafkas Univ., Kars, Turkey
S. Kazımoğlu Kafkas Univ., Kars, Turkey
M. Çağlar ErzurumTechn.Univ.,Turkey

DOI: https://doi.org/10.37863/umzh.v73i11.1014

Keywords: Normalized Bessel functions of the first kind, , convex function, starlike function, zeros of Bessel function derivative, Radius

Abstract

UDC 517.5

In this paper, our aim is to find the radii of starlikeness and
convexity of Bessel function derivatives for three different kind of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for $n$th derivative of Bessel function and
properties of real zeros of it. In addition, by using the Euler–Rayleigh inequalities we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero for the normalized $n$th derivative of Bessel function. The main results of the paper are natural extensions of some known results on classical Bessel functions of the first kind.

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