Nonlinear Triple Product $A^{*}B + B^{*}A$ for Derivations on $\ast$-Algebras

Let $\mathcal{A}$ be a prime $\ast$-algebra. In this paper, assuming that $\Phi:\mathcal{A}\to\mathcal{A}$ satisfies
$$\Phi(A\diamond B \diamond C)=\Phi(A)\diamond B \diamond C+A\diamond\Phi(B) \diamond C+A \diamond B \diamond \Phi(C)$$
where $A\diamond B = A^{*}B + B^{*}A$ for all $A,B\in\mathcal{A}$, we prove that $\Phi$ is additive an $\ast$-derivation.