Jordan and Lie derivations of $\phi$-Johnson amenable Banach algebras

Let U be a $\phi$-Johnson amenable Banach algebra in which $\phi$ is a non-zero multiplicative linear functional on U. Suppose that X is a Banach U-bimodule such that $a\mathrm{.}x=\phi (a)x$ for all a in U and x in X or $x\mathrm{.}a=\phi (a)x$ 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.