$n$-ary Hom-Nambu algebras

In this paper, we define $\omega$-derivations, and study some properties of $\omega$-derivations, with its properties we can structure a new $n$-ary Hom-Nambu algebra from an $n$-ary Hom-Nambu algebra. In addition, we also give derivations and representations of $n$-ary Hom-Nambu algebras.