Maps preserving the coincidence points of operators

Let $\mathcal{B(X)}$ be the algebra of all bounded linear operators on a Banach space $\mathcal{X}$ with $\dim \mathcal{X} \geqslant 2$. In this paper, we describe surjective maps $\phi: \mathcal{B(X)}\to\mathcal{B(X)}$ preserving the coincidence points of operators, i.e., $C(A,B)=C(\phi(A),\phi(B))$, for every $A, B \in \mathcal{B(X)}$, where $C(A,B)$ denotes the set of all coincidence points of two operators $A$ and $B$.