Twisted Rota-Baxter operators on 3-Leibniz algebras and NS-3-Leibniz algebras

The purpose of this paper is to introduce the cohomology and deformations of twisted Rota-Baxter operators on 3-Leibniz algebras and NS-3-Leibniz algebras. We construct an $L_\infty$-algebra whose Maurer-Cartan elements are twisted Rota-Baxter operators, and we define the cohomology of a twisted Rota-Baxter operator. Then we consider formal and order $n$ deformations of twisted Rota-Baxter operators from cohomological points of view. Finally, we introduce and study NS-3-Leibniz algebras as the underlying structure of twisted Rota-Baxter operators on 3-Leibniz algebras.