Superstability of homomorphisms and derivations on C*-algebras: A fixed point approach.

Let A be a unital C*-algebras, B be a Banach algebra and let X be a Banach A-module. By using fixed point methods, we prove that: i) Every almost linear mapping h : A → B which satisfies h(2nuy) = h(2nu)h(y) for all u ∈ A+, all y ∈ A, and all n = 0, 1,2,…, is a homomorphism. ii) Every almost linear continuous mapping d : A → X is a derivation when d(2nuy) = d(2nu)y + 2nud(y) holds for all u ∈ A+, all u ∈ A, and all n = 0, 1, 2,…. [ABSTRACT FROM AUTHOR]