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- MakaleAçık Erişim2017Scopus SJRQ2Bounds for the radii of univalence of some special functions
Aktaş, Ibrahim; Baricz, Árpád; Yaǧmur, Nihat
Tight lower and upper bounds for the radii of univalence (and starlikeness) of some normalized Bessel, Struve and Lommel functions of the first kind are obtained via Euler-Rayleigh inequalities. It is shown also that the radius of univalence of the Struve functions is greater than the corresponding radius of univalence of Bessel functions. Moreover, by using the idea of Kreyszig and Todd, and Wilf it is proved that the radii of univalence of some normalized Struve and Lommel functions are exactly the radii of starlikeness of the same functions, and they are actually solutions of some functional equations. The Laguerre-Pólya class of entire functions plays an important role in our study.
AtıfScopus35WoS34OpenAlex22İncele - MakaleAçık Erişim2017Scopus SJRQ2Bounds for Radii of Starlikeness of Some q -Bessel Functions
Aktaş, İbrahim; Baricz, Árpád
In this paper the radii of starlikeness of Jackson’s second and third q-Bessel functions are considered and for each of them three different normalization are applied. By applying Euler–Rayleigh inequalities for the first positive zeros of these functions tight lower and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre–Pólya class of real entire functions plays an important role in this study. In particular, we obtain some new bounds for the first positive zero of the derivative of the classical Bessel function of the first kind.
AtıfScopus38WoS38OpenAlex38İncele