Nonlinear maps preserving the first mixed jordan triple product on *-algebras

Let [Formula: see text] and [Formula: see text] represent two unital *-algebras such that [Formula: see text] possesses a nontrivial projection. In the present article, we study, under certain mild assumptions, if a bijective map [Formula: see text] satisfies [Formula: see text] for all [Formula: see text], then [Formula: see text] is a *-preserving ring isomorphism. Furthermore, this result is investigated on factor von Neumann algebras.