  Recently, CQ method has been investigated extensively. However, it is mainly
applied to modify Mann, Ishikawa and Halpern iterations to get strong
convergence. In this paper, we study the properties of CQ method and proposed a
framework. Based on that, we obtain a series of strong convergence theorems.
Some of them are the extensions of previous results. On the other hand, CQ
method, monotone Q method, monotone C method and monotone CQ method, used to be
given separately, have the following relations: CQ method TRUE $\Rightarrow$
monotone Q method TRUE $\Rightarrow$ monotone C method TRUE $\Leftrightarrow$
monotone CQ method TRUE.
