Let \(T_{d}^{\theta }\) be a bilinear Dunkl-generalized fractional integral operator, and \(T_{d,\vec {b}}^{\theta }\) be a commutator formed by \(\vec {b}=(b_{1},b_{2})\in (\text {BMO} _{d} (\mathbb {R}^{N}))^{2} \) and the \(T_{d}^{\theta }\) . In this setting, we prove that the \(T_{d}^{\theta }\) is bounded from product of Dunkl-Morrey spaces \(\mathcal {M}^{p_{1},q_{1}}_{d}(\mathbb {R}^{N})\times \mathcal {M}^{p_{2},q_{2}}_{d}(\mathbb {R}^{N})\) into spaces \(\mathcal {M}^{p,q}_{d}(\mathbb {R}^{N})\) , and it is also bounded from product of generalized Dunkl-Morrey spaces \(\mathcal {L}^{\varphi _{1},p_{1}}_{d}(\mathbb {R}^{N})\times \mathcal {L}^{\varphi _{2},p_{2}}_{d}(\mathbb {R}^{N})\) into spaces \(\mathcal {L}^{\varphi ,p}_{d}(\mathbb {R}^{N})\) , where \(\frac{1}{p}=\frac{1}{p_{1}}+\frac{1}{p_{2}}-2\theta \) with \(1<p_{i}<\frac{1}{\theta _{i}}\) , \(\frac{1}{q}=\frac{1}{q_{1}}+\frac{1}{q_{2}}-2\theta \) for \(1<q_{i}<\frac{1}{\theta _{i}}\) , \(i=1,2\) , and Lebesgue measurable functions \(\varphi _{1}, \varphi _{2}\) and \(\varphi \) belong to class \(\mathbb {W}^{\delta }_{d}\) for \(\delta \in (0,2)\) and satisfy \(\varphi _{1}\varphi _{2}=\varphi \) . Furthermore, the boundedness of the commutator \(T_{d,\vec {b}}^{\theta }\) on product of spaces \(\mathcal {M}^{p_{1},q_{1}}_{d}(\mathbb {R}^{N})\times \mathcal {M}^{p_{2},q_{2}}_{d}(\mathbb {R}^{N})\) and on product of spaces \(\mathcal {L}^{\varphi _{1},p_{1}}_{d}(\mathbb {R}^{N})\times \mathcal {L}^{\varphi _{2},p_{2}}_{d}(\mathbb {R}^{N})\) is also obtained.
