Abstract
Let R be a noncommutative prime ring, U be the left Utumi quotient ring of R, and k, m, n, r be fixed positive integers. If there exist a generalized derivation G and a derivation g (which is independent of G) of R such that [G(x(m))x(n)+x(n)g(x(m)), x(r)](k)=0, for all x is an element of R, then there exists a is an element of U such that G(x)=ax, for all xR. As a consequence of the result in the present article, one may obtain Theorem 1 in Demir and Argac [10].