Generalized skew derivations on Lie ideals in prime rings

Let R be a prime ring of characteristic different from 2 and 3, L a noncentral Lie ideal of R, F a nonzero generalized skew derivation of R and n≥ 1 be a fixed integer such that [F(u) , u] ⁿ = 0 for all u∈ L. Suppose that R does not satisfy s ₄ , then either there exists an element a in C such that F(x) = ax for all x∈ R or there exists a∈ C and b∈ Q such that F(x) = ax+ [b, x] for all x∈ R.