On the real line, the Dunkl operators are differential-difference operators associated with the reflection group \(\mathbb {Z}_{2}\) on \(\mathbb {R}\) . In this paper, for \(\gamma >0\) , we prove the boundedness of the Dunkl Bessel Riesz operator \(I_{\alpha ,\gamma }^{\nu }\) from the generalized Lebesgue space \(L^{p}(\mathbb {R},d\mu _{\nu })\) into the generalized Lebesgue space \(L^{q}(\mathbb {R},d\mu _{\nu })\) , where \(d\mu _\nu \) is the weighted Lebesgue measure on \(\mathbb {R}\) . Also under appropriate assumptions, we obtain the boundedness of \(I_{\alpha ,\gamma }^{\nu }\) from the Dunkl-type Morrey space \(L^{p_1,q_1}(\mathbb {R},d\mu _\nu )\) into Dunkl-type Morrey space \(L^{p_2,q_2}(\mathbb {R},d\mu _\nu )\) .
