Cohomology, deformations and extensions of Rota-Baxter Leibniz algebras

A Rota-Baxter Leibniz algebra is a $(\mathfrak{g},[~,~]_{\mathfrak{g}})$ equipped with operator $T : \mathfrak{g} \rightarrow \mathfrak{g}$. We define representation and dual of algebras. Next, we cohomology theory also study the infinitesimal formal deformation algebras show that our cohomology. Moreover, an abelian extension equivalence classes such extensions are related to groups.