Let $ R $ denote a prime ring with characteristic not 2, let $ n\geq 1 $ be a fixed integer,let $ L $ be a Lie ideal of $ R $ , and let $ C $ be the extended centroid of $ R $ .Let $ F $ and $ G $ represent two generalized skew derivations of $ R $ satisfying $ (F(xy)-G(x)y-yx)^{n}=0 $ for all $ x,y\in L $ .Then $ L $ is central, unless $ R $ satisfies the standard polynomial identity $ s_{4}(x_{1},\dots,x_{4})=0 $ .
