Nearly Jordan *-Homomorphisms between Unital C*-Algebras.

Let A, B be two unital C*-algebras. We prove that every almost unital almost linear mapping h : A → B which satisfies h(3ⁿuy+3ⁿyu) = h(3ⁿu)h(y)+h(y)h(3ⁿu) for all u ∈ U(A), all y ∈ A, and all n = 0, 1, 2,…, is a Jordan homomorphism. Also, for a unital C*-algebra A of real rank zero, every almost unital almost linear continuous mapping h : A → B is a Jordan homomorphism when h(3ⁿuy+3ⁿyu) = h(3ⁿu)h(y)+h(y)h(3ⁿu) holds for all u ∈ I₁ (A_sa), all y ∈ A, and all n = 0, 1, 2,…. Furthermore, we investigate the Hyers- Ulam-Aoki-Rassias stability of Jordan *-homomorphisms between unital C*-algebras by using the fixed points methods. [ABSTRACT FROM AUTHOR]