Let A and B be two unital C∗-algebras such that A contains a non-trivial projection P1. In this paper, we investigate the additivity of maps Φ from A onto B that are bijective maps, that satisfy Φ AB∗C + CB∗A 2 = Φ(A)Φ(B) ∗ Φ(C) + Φ(C)Φ(B) ∗ Φ(A) 2 for every A, B,C ∈ A. Moreover if B is a prime C∗-algebra and Φ(I ) is a positive element, then Φ is a ∗-isomorphism.
