The Classical Hom-Leibniz Yang-Baxter Equation and Hom-Leibniz Bialgebras

In this paper, we first introduce the notion of Hom-Leibniz bialgebras, which is equivalent to matched pairs of Hom-Leibniz algebras and Manin triples of Hom-Leibniz algebras. Additionally, we extend the notion of relative Rota-Baxter operators to Hom-Leibniz algebras and prove that there is a Hom-pre-Leibniz algebra structure on Hom-Leibniz algebras that have a relative Rota-Baxter operator. Finally, we study the classical Hom-Leibniz Yang-Baxter equation on Hom-Leibniz algebras and present its connection with the relative Rota-Baxter operator.