  We consider the split convex feasibility problem in a fixed point setting.
Motivated by the well-known CQ-method of Byrne (2002), we define an abstract
andweber transform which applies to more general operators than the metric
projection. We call the result of this transform a Landweber operator. It turns
out that the Landweber transform preserves many interesting properties. For
example, the Landweber transform of a (quasi/firmly) nonexpansive mapping is
again (quasi/firmly) nonexpansive. Moreover, the Landweber transform of a
(weakly/linearly) regular mapping is again (weakly/linearly) regular. The
preservation of regularity is important because it leads to (weak/linear)
convergence of many CQ-type methods.
