Lie Triple Derivable Mappings on Rings

Let ? be a ring containing a nontrivial idempotent. In this article, under a mild condition on ?, we prove that if δ is a Lie triple derivable mapping from ? into ?, then there exists a Z _{A, B} (depending on A and B) in its centre 𝒵(?) such that δ(A + B) = δ(A) + δ(B) + Z _{A, B} . In particular, let ? be a prime ring of characteristic not 2 containing a nontrivial idempotent. It is shown that, under some mild conditions on ?, if δ is a Lie triple derivable mapping from ? into ?, then δ = D + τ, where D is an additive derivation from ? into its central closure T and τ is a mapping from ? into its extended centroid 𝒞 such that τ(A + B) = τ(A) + τ(B) + Z _{A, B} and τ(A, B], C]) = 0 for all A, B, C ∈ ?.