  We consider sequential iterative processes for the common fixed point problem
of families of cutter operators on a Hilbert space. These are operators that
have the property that, for any point x\inH, the hyperplane through Tx whose
normal is x-Tx always "cuts" the space into two half-spaces one of which
contains the point x while the other contains the (assumed nonempty) fixed
point set of T. We define and study generalized relaxations and extrapolation
of cutter operators and construct extrapolated cyclic cutter operators. In this
framework we investigate the Dos Santos local acceleration method in a unified
manner and adopt it to a composition of cutters. For these we conduct
convergence analysis of successive iteration algorithms.
