Additive maps preserving the fixed points of Jordan products of operators

Let $\mathcal{B(X)}$ be the algebra of all bounded linear operators on a complex Banach space $\mathcal{X}$. In this paper, we determine the form of a surjective additive map $\phi: \mathcal{B(X)} \rightarrow \mathcal{B(X)}$ preserving the fixed points of Jordan products of operators, i.e., $F(AoB) \subseteq F(\phi(A) o\phi(B))$, for every $A,B \in \mathcal{B(X)}$, where $AoB=AB+BA$, and $F(A)$ denotes the set of all fixed points of operator $A$.