On Lie ideals and Jordan generalized derivations of prime rings

Let R be a ring and S a nonempty subset of R. An additive mapping F: R --> R is called a generalized derivation (resp. Jordan generalized derivation) on S if there exists a derivation d: R --> R such that F(xy) = F(x)y+xd(y) (resp. F(x(2))=F(x)x+xd(x)) holds for all x, y is an element of S. Suppose that R is a 2-torsion free prime ring and U a nonzero Lie ideal of R such that u(2) is an element of U for all u is an element of U. In the present paper it is shown that if F is a Jordan generalized derivation on U, then F is a generalized derivation on U.