Automorphisms and generalized skew derivations which are strong commutativity preserving on polynomials in prime and semiprime rings

Let R be a prime ring of characteristic different from 2, Q (r) its right Martindale quotient ring and C its extended centroid. Suppose that F, G are generalized skew derivations of R with the same associated automorphism alpha, and p(x (1), aEuro broken vertical bar, x (n) ) is a non-central polynomial over C such that for all x, y a p(r (1), aEuro broken vertical bar, r (n) ): r (1), aEuro broken vertical bar, r (n) a R. Then there exists lambda a C such that F(x) = G(x) = lambda I +/-(x) for all x a R.