## Abstract

Recently, Colao et al. (J Math Anal Appl 344:340-352, 2008) introduced a hybrid viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a finite family of nonexpansive mappings in a real Hilbert space. In this paper, by combining Colao, Marino and Xu's hybrid viscosity approximation method and Yamada's hybrid steepest-descent method, we propose a hybrid iterative method for finding a common element of the set GMEP of solutions of a generalized mixed equilibrium problem and the set ∩^{N}_{i=1} Fix (S _{i}) of fixed points of a finite family of nonexpansive mappings {S_{i}}^{N}_{i = 1} in a real Hilbert space. We prove the strong convergence of the proposed iterative algorithm to an element of ∩^{N}_{i=1} Fix (S^{i}) ∩ GMEP, which is the unique solution of a variational inequality.

Original language | English |
---|---|

Article number | 92 |

Journal | Fixed Point Theory and Applications |

Volume | 2012 |

DOIs | |

State | Published - 2012 |

Externally published | Yes |

## Keywords

- Fixed point
- Generalized mixed equilibrium problem
- Hybrid iterative method
- Nonexpansive mapping
- Variational inequality