Jordan Left Derivations on Lie Ideals of Prime Γ−rings

.Let M be a 2-torsion free prime Γ-ring. Let U be a Lie ideal of M such that uαu ∈ U, for all u ∈ U and α ∈ Γ. If d : M → M is an additive mapping such that d(uαu) = 2uαd(u), for all u ∈ U and α ∈ Γ, then d(uαv) = uαd(v) + vαd(u), for all u, v ∈ U and α ∈ Γ