Abstract
In the present paper, our aim is to prove the following result: Let R be a noncommutative prime ring, I a nonzero ideal of R, F a generalized derivation of R, and n >= 1 a fixed integer. If 0 not equal p such that p(F(x)F(y) - xy)(n) = 0 for all x, y is an element of I, then there exists lambda is an element of C such that F(x) = lambda x for all x is an element of R with lambda(2n) = 1.