  In this paper, we introduce the concepts of Rota-Baxter operators and
differential operators with weights on a multiplicative $n$-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.
