Nonlinear Triple Product A*B + B*A for Derivations on -Algebras

Let A be a prime -algebra. In this paper, assuming that Φ:A satisfies Φ(A B C)=Φ(A) B C+AΦ(B) C+A B Φ(C) where A B = A*B + B*A for all A,B , we prove that Φ is additive an -derivation.