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- MakaleAçık Erişim2018Bounds for radii of starlikeness and convexity of some special functions
Aktaş, Ibrahim; Baricz, Árpád; Orhan, Halit
In this paper we consider some normalized Bessel, Struve, and Lommel functions of the first kind and, by using the Euler-Rayleigh inequalities for the first positive zeros of a combination of special functions, we obtain tight lower and upper bounds for the radii of starlikeness of these functions. By considering two different normalizations of Bessel and Struve functions we give some inequalities for the radii of convexity of the same functions. On the other hand, we show that the radii of univalence of some normalized Struve and Lommel functions are exactly the radii of starlikeness of the same functions. In addition, by using some ideas of Ismail and Muldoon we present some new lower and upper bounds for the zeros of derivatives of some normalized Struve and Lommel functions. The Laguerre-Pólya class of real entire functions plays an important role in our study.
- MakaleAçık Erişim2017Bounds 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.