  We prove that the spherical mean value of the Dunkl-type generalized
translation operator $\tau^y$ is a positive $L^p$-bounded generalized
translation operator $T^t$. As application, we prove the Young inequality for a
convolution defined by $T^t$, the $L^p$-boundedness of $\tau^y$ on a radial
functions for $p>2$, the $L^p$-boundedness of the Riesz potential for the Dunkl
transform and direct and inverse theorems of approximation theory in
$L^p$-spaces with the Dunkl weight.
