Nearly Jordan ∗‐Homomorphisms between Unital C∗‐Algebras

Let , be two unital ∗-algebras. We prove that every almost unital almostlinear mapping ℎ : → which satisfies ℎ(3+3)=ℎ(3)ℎ()+ℎ()ℎ(3) for all ∈(), all ∈, and all =0,1,2,…, is a Jordan homomorphism. Also, for a unital∗-algebra of real rank zero, every almost unital almost linear continuous mapping ℎ∶→ is a Jordan homomorphism when ℎ(3+3)=ℎ(3)ℎ()+ℎ()ℎ(3) holdsfor all ∈1(sa), all ∈, and all =0,1,2,…. Furthermore, we investigate the Hyers-Ulam-Aoki-Rassias stability of Jordan ∗-homomorphisms between unital ∗-algebras by using the fixed points methods