## Abstract

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∈H, 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 a convergence analysis of successive iteration algorithms.

Original language | English |
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Pages (from-to) | 809-818 |

Number of pages | 10 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 394 |

Issue number | 2 |

DOIs | |

State | Published - 15 Oct 2012 |

## Keywords

- Common fixed point
- Cutter operator
- Cyclic projection method
- Dos Santos local acceleration
- Quasi-nonexpansive operators

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics