Bounds for radii of starlikeness and convexity of some special functions

Abstract

In this paper we consider some normalized Bessel, Struve, and Lommel functions of the rst kind and, byusing the Euler{Rayleigh inequalities for the rst positive zeros of a combination of special functions, we obtain tightlower and upper bounds for the radii of starlikeness of these functions. By considering two different normalizations ofBessel and Struve functions we give some inequalities for the radii of convexity of the same functions. On the otherhand, we show that the radii of univalence of some normalized Struve and Lommel functions are exactly the radii ofstarlikeness of the same functions. In addition, by using some ideas of Ismail and Muldoon we present some new lowerand upper bounds for the zeros of derivatives of some normalized Struve and Lommel functions. The Laguerre{P?olyaclass of real entire functions plays an important role in our study.