Rota–Baxter multiplicative 3-ary Hom-Nambu–Lie algebras

In this paper, we introduce the concepts of Rota–Baxter operators and differential operators with weights on a multiplicative nn-ary Hom-algebra. We then focus on Rota–Baxter multiplicative 3-ary Hom-Nambu–Lie algebras and show that they can be derived from Rota–Baxter Hom-Lie algebras, Hom-preLie algebras and Rota–Baxter commutative Hom-associative algebras. We also explore the connections between these Rota–Baxter multiplicative 3-ary Hom-Nambu–Lie algebras.