A Note on Nonlinear Mixed Type Product E ⋄ K, D∗ on ∗-Algebras

Let B be a ∗-algebra with the unity and a nontrivial projection. In the present paper, we show under certain restrictions that if a map Ψ : B →B satisfies Ψ(E ⋄ K, D∗) = Ψ(E) ⋄ K, D∗ + E ⋄Ψ(K), D∗ + E ⋄ K, Ψ(D)∗ for all E, K, D ∈ B, then Ψ is an additive ∗-derivation.