In this note our aim is to determine the radius of starlikeness of the normalized Bessel functions of the first kind for three different kinds of normalization. The key tool in the proof of our main result is the Mittag-Leffler expansion for Bessel functions of the first kind and the fact that, according to Ismail and Muldoon [IM2], the smallest positive zeros of some Dini functions are less than the first positive zero of the Bessel function of the first kind.File: starlikeness.tex, printed: 2018-011-05, 0.51 2010 Mathematics Subject Classification. 30C45, 33C10. Key words and phrases. Bessel and modified Bessel functions of the first kind; univalent, starlike and convex functions.A.
Abstract. In this paper monotonicity results concerning the gamma function are deduced. These results lead to inequalities which improve some known bounds for the Γ function.Mathematics subject classification (2010): 33B15.
We determine in this paper new results about the radius of uniform convexity of two kinds of normalization of the Bessel function Jν in the case ν∈(−2,−1), and provide an alternative proof regarding the radius of convexity of order alpha. We then compare results regarding the convexity and uniform convexity of the considered functions and determine interesting connections between them.
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