Additivity of maps preserving products AP PA^* on C^*-algebras

Let A and B be two prime C^*-algebras. In this paper, we investigate the additivity of map Φ from A onto B that are bijective unital and satisfies Φ (AP+λPA^*) =Φ (A) Φ (P) +λΦ (P) Φ (A) ^*, for all A and P\P₁, I₀-P₁\ where P₁ is a nontrivial projection in A and λ\-1, +1\. Then, Φ is *-additive.