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\begin{document}$$ \mathcal {A} $$\end{document} and B\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {B}$$\end{document} be two unital C∗\documentclass[12pt]{minimal}
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\begin{document}$$C^*$$\end{document}-algebras such that A\documentclass[12pt]{minimal}
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\begin{document}$$ \mathcal {A} $$\end{document} contains a non-trivial projection P1\documentclass[12pt]{minimal}
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\begin{document}$$P_1$$\end{document}. In this paper, we investigate the additivity of maps Φ\documentclass[12pt]{minimal}
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\begin{document}$$ \varPhi $$\end{document} from A\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {A}$$\end{document} onto B\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {B}$$\end{document} that are bijective maps, that satisfy ΦAB∗C+CB∗A2=Φ(A)Φ(B)∗Φ(C)+Φ(C)Φ(B)∗Φ(A)2\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \varPhi \left( \frac{AB^*C+CB^*A}{2} \right) =\frac{\varPhi (A)\varPhi (B)^*\varPhi (C)+\varPhi (C)\varPhi (B)^*\varPhi (A)}{2} \end{aligned}$$\end{document}for every A,B,C∈A\documentclass[12pt]{minimal}
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\begin{document}$$ A, B, C\in \mathcal {A}$$\end{document}. Moreover if B\documentclass[12pt]{minimal}
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\begin{document}$$ \mathcal {B} $$\end{document} is a prime C∗\documentclass[12pt]{minimal}
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\begin{document}$$C^*$$\end{document}-algebra and Φ(I)\documentclass[12pt]{minimal}
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\begin{document}$$ \varPhi (I)$$\end{document} is a positive element, then Φ\documentclass[12pt]{minimal}
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\begin{document}$$ \varPhi $$\end{document} is a ∗\documentclass[12pt]{minimal}
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\begin{document}$$*$$\end{document}-isomorphism.
