  In this paper certain Tur\'an type inequalities for some Lommel functions of
the first kind are deduced. The key tools in our proofs are the infinite
product representation for these Lommel functions of the first kind, a
classical result of G. P\'olya on the zeros of some particular entire
functions, and the connection of these Lommel functions with the so-called
Laguerre-P\'olya class of entire functions. Moreover, it is shown that in some
cases J. Steinig's results on the sign of Lommel functions of the first kind
combined with the so-called monotone form of l'Hospital's rule can be used in
the proof of the corresponding Tur\'an type inequalities.
