Graded modal operators and fixed points

There is the well-known Fixed Point Theorem in the theory of modal logics. In the article this theorem is generalized from monomodal case to graded modalities. The following theorem is proved
Theorem. For any graded modalized operator $F_\varphi$, there is unique fixed point of the operator $F_\varphi$ in every strictly partially ordered model with the ascending chain condition and there is a graded formula $\omega$, which defines the fixed point in every such model. The formula $\omega$ contains only those graded modalities, which are contained in $\varphi$.