Jordan and Lie derivations of φ-Johnson amenable Banach algebras

Let U be a φ-Johnson amenable Banach algebra in which φ is a non-zero multiplicative linear functional on U. Suppose that X is a Banach U-bimodule such that a.x=φ(a)x for all a in U and x in X or x.a=φ(a)x for all a in U and x in X. We show that every continuous Jordan derivation from U to X is a derivation, and every continuous Lie derivation from U to X decomposed into the sum of a continuous derivation and a continuous center-valued trace.