Generalized skew-derivations acting on multilinear polynomial in prime rings

Let (Formula presented.) be a noncommutative prime ring of characteristic different from 2, (Formula presented.) be the right Martindale quotient ring of (Formula presented.) and (Formula presented.) be the extended centroid of (Formula presented.). Suppose that (Formula presented.) is a noncentral multilinear polynomial over (Formula presented.) and (Formula presented.) are three generalized skew-derivations of (Formula presented.) associated to the same automorphism α. Let (Formula presented.) be the associated skew derivations respectively of (Formula presented.) and (Formula presented.) such that h, f, g are commuting with α. We will provide the complete description of (Formula presented.) and (Formula presented.), in the case (Formula presented.) for all (Formula presented.).