Some results on compatible ternary Leibniz algebras

In this paper, we introduce compatible ternary Leibniz algebras, (dual)Nijenhuis pairs from the second-order deformation of ternary Leibniz algebras with a representarion and study the invariance of certains operators (generalized derivations, Rota-Baxter operators, Reynolds operators, element of centroid, averaging operators, Nijenhuis operators) whenever we go from Leibniz algebras to ternary Leibniz algebras. We also give contructions of (compatible) ternary Leibniz algebras either from averaging operators, modules or O-operator.