Nonlinear mixed bi-skew Lie triple derivations on factor von Neumann algebras

Let [Formula: see text] be a factor von Neumann algebra with dim[Formula: see text]. In this paper, we prove that a map [Formula: see text] satisfies [Formula: see text] for all [Formula: see text] if and only if there exists a real number [Formula: see text] such that [Formula: see text], where [Formula: see text] is an additive ∗-derivation and [Formula: see text].