  Tight lower and upper bounds for the radius of univalence 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. The
Laguerre-P\'olya class of entire functions plays an important role in our
study.
