Let A be a Banach algebra and X be a compact Hausdor space. For given homomorphisms 2 Hom(A) and 2 Hom(C(X;A)), we introduce homomorphisms ˜ 2 Hom(C(X;A)) and ˜x 2 Hom(A), where x 2 X. We then study both ˜-(weak) amenability of C(X;A), and ˜x-(weak) amenability of A.