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.

The objective of this paper is to introduce the notion of skew Lie centralizers in *-rings, and to investigate the structure of skew Lie centralizers and strong skew commutativity preserving maps in prime *-rings without assuming the existence of a symmetric idempotent and the unital element. As an application, we shall characterize such maps in different operator algebras.