Two generalized derivations on Lie ideals in prime rings

Let $R$ be a prime ring of characteristic not equal to $2$, $U$ the Utumi quotient and $C$ extended centroid $R$. $G$ $F$ two generalized derivations on $L$ non-central Lie ideal If $F\Big(G(u)\Big)u = G(u^{2})$ for all $u \in L$, then one following holds: (1) $G=0$. (2) There exist $p,q U$ such that $G(x)=p x$, $F(x)=qx$ $x R$ with $qp=p$. (3) satisfies $s_4$.