Generalized derivations preserving Engel condition in prime and semiprime rings

Let Script capital R be a prime ring with char(Script capital R)not equal 2, Script capital L a non-central Lie ideal of Script capital R, Q its Martindale quotient ring and C its extended centroid. Let F : Script capital R -> Script capital R and G : Script capital R -> Script capital R be nonzero generalized derivations on Script capital R such that [F(x),F(y)]k = G([x,y]k),for all x,y is an element of Script capital L. Then there exists lambda is an element of C such that F(x) = lambda x and G(x) = lambda k+1x, for any x is an element of Script capital R, unless Script capital R subset of M2((C) over bar), where (C) over bar over bar is the algebraic closure of c.