A note on the generalized Jordan triple derivations on Lie ideals in semiprime rings

Let R be an associative ring, and F : R ! R an additive mapping. The map F is called a Jordan triple derivation if F (xyx) = F (x)yx + xF (y)x + xyF (x) for all x, y 2 R which is fulfilled (2), and F is called a generalized Jordan triple derivation if F (xyx) = F (x)yx + xf (y)x + xyf (x) with some Jordan triple derivation f for all x, y 2 R which is fulfilled (13). In this note, we deal with generalized Jordan triple derivations of semiprime rings, and give an affirmative answer to our conjecture in (12).