Let A and B be two prime complex ∗-algebras. We proved that every bijective mapping Φ : A → B satisfying Φ(a ¦ b + b∗a) = Φ(a) ¦ Φ(b)+Φ(b)∗Φ(a) (resp., Φ(a∗ ¦ b+ab∗) = Φ(a)∗ ¦ Φ(b)+Φ(a)Φ(b)∗), where a ¦ b = ab + ba∗, for all elements a, b ∈ A, is a ∗-ring isomorphism.
