A result on generalized derivations on right ideals of prime rings

Let R be a prime ring of characteristic other than 2 and let I be a nonzero right ideal of R. Also let U be the right Utumi quotient ring of R and let C be the center of U. If G is a generalized derivation of R such that [[G(x), x], G(x)] = 0 for all x ∈ I, then R is commutative or there exist a, b ∈ U such that G(x) = ax + xb for all x ∈ R and one of the following assertions is true: (1) (a - λ)I = (0) = (b + λ)I for some λ ∈ C,(2) (a - λ)I = (0) for some λ ∈ C and b ∈ C.