A note on generalized derivations on prime rings

Let R be a prime ring with the extended centroid C and symmetric Martindale quotient ring $$Q_s(R)$$ . In this paper we prove the following result. Let $$F: R \rightarrow R$$ be a generalized derivation associated with a non-zero derivation d on R and let h be an additive map of R such that $$F(x)x=xh(x)$$ for all $$x\in R$$ . Then either R is commutative or $$F(x)=xp$$ and $$h(x)=px$$ where $$p\in Q_{s}(R)$$ .