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We consider sequential iterative processes for the common fixed point problemof families of cutter operators on a Hilbert space. These are operators thathave the property that, for any point x\inH, the hyperplane through Tx whosenormal is x-Tx always "cuts" the space into two half-spaces one of whichcontains the point x while the other contains the (assumed nonempty) fixedpoint set of T. We define and study generalized relaxations and extrapolationof cutter operators and construct extrapolated cyclic cutter operators. In thisframework we investigate the Dos Santos local acceleration method in a unifiedmanner and adopt it to a composition of cutters. For these we conductconvergence analysis of successive iteration algorithms.

Extrapolation and Local Acceleration of an Iterative Process for Common Fixed Point Problems