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**An extragradient-like approximation method for variational inequality problems and fixed point problems.**
*(English)*
Zbl 1124.65056

Summary: The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping. The authors introduce an extragradient-like approximation method based on the so-called extragradient method and a viscosity approximation method. A strong convergence theorem is proved for two iterative sequences generated by this method.

### MSC:

65K10 | Numerical optimization and variational techniques |

49J40 | Variational inequalities |

47H10 | Fixed-point theorems |

49M25 | Discrete approximations in optimal control |

47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |

### Keywords:

extragradient-like approximation method; variational inequality; fixed point; monotone mapping; nonexpansive mapping; strong convergence### References:

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