Additivity of Jordan n-tuple maps on rings

Let $$\mathfrak {R}$$ and $$\mathfrak {R}'$$ be rings. We study the additivity of surjective maps $$M:\mathfrak {R}\rightarrow \mathfrak {R}'$$ and $$M^{*}:\mathfrak {R}'\rightarrow \mathfrak {R}$$ preserving a type of Jordan n-tuple product on these rings. We prove that if $$\mathfrak {R}$$ contains a non-trivial idempotent satisfying some conditions, then they are additive. In particular, if $$\mathfrak {R}$$ is a standard operator algebra, then both M and $$M^{*}$$ are additive.