Let U be a φ-Johnson amenable Banach algebra in which φ is a nonzero multiplicative linear functional on U. Suppose that X is a Banach U-bimodule such that a.x = φ(a)x for all a ∈ U, x ∈ X or x.a = φ(a)x for all a ∈ U, x ∈ 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 centervalued trace. Then we apply our results for character amenable Banach algebras and amenable Banach algebras. We also provide some results about φ-Johnson amenability, especially we give some conditions equivalent to φ-Johnson amenability
