3-Bihom-ρ-Lie Algebras, 3-Pre-Bihom-ρ-Lie Algebras

The purpose is to introduce the notions of 3-Bihom-ρ-Lie algebras and 3-preBihom-ρ-Lie algebras. The authors describe their constructions and express the related lemmas and theorems. Also, they define the 3-Bihom-ρ-Leibniz algebras and show that a3-Bihom-ρ-Lie algebra is a 3-Bihom-ρ-Leibniz algebra with the ρ-Bihom-skew symmetry property. Moreover, a combination of a 3-Bihom-ρ-Lie algebra bracket and a Rota-Baxer operator gives a 3-pre-Bihom-ρ-Lie algebra structure.