### Abstract

In this paper, we introduce an iterative process which converges strongly to a common element of set of common fixed points of countably infinite family of closed relatively quasi- nonexpansive mappings, the solution set of generalized equilibrium problem and the solution set of the variational inequality problem for a γ-inverse strongly monotone mapping in Banach spaces. Our theorems improve, generalize, unify and extend several results recently announced.

Original language | English |
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Pages (from-to) | 3439-3449 |

Number of pages | 11 |

Journal | Applied Mathematics and Computation |

Volume | 216 |

Issue number | 12 |

DOIs | |

Publication status | Published - Aug 15 2010 |

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### All Science Journal Classification (ASJC) codes

- Computational Mathematics
- Applied Mathematics

### Cite this

*Applied Mathematics and Computation*,

*216*(12), 3439-3449. https://doi.org/10.1016/j.amc.2010.02.054

}

*Applied Mathematics and Computation*, vol. 216, no. 12, pp. 3439-3449. https://doi.org/10.1016/j.amc.2010.02.054

**Convergence theorems for equilibrium problem, variational inequality problem and countably infinite relatively quasi-nonexpansive mappings.** / Zegeye, Habtu; Ofoedu, Eric U.; Shahzad, Naseer.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Convergence theorems for equilibrium problem, variational inequality problem and countably infinite relatively quasi-nonexpansive mappings

AU - Zegeye, Habtu

AU - Ofoedu, Eric U.

AU - Shahzad, Naseer

PY - 2010/8/15

Y1 - 2010/8/15

N2 - In this paper, we introduce an iterative process which converges strongly to a common element of set of common fixed points of countably infinite family of closed relatively quasi- nonexpansive mappings, the solution set of generalized equilibrium problem and the solution set of the variational inequality problem for a γ-inverse strongly monotone mapping in Banach spaces. Our theorems improve, generalize, unify and extend several results recently announced.

AB - In this paper, we introduce an iterative process which converges strongly to a common element of set of common fixed points of countably infinite family of closed relatively quasi- nonexpansive mappings, the solution set of generalized equilibrium problem and the solution set of the variational inequality problem for a γ-inverse strongly monotone mapping in Banach spaces. Our theorems improve, generalize, unify and extend several results recently announced.

UR - http://www.scopus.com/inward/record.url?scp=77953614828&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953614828&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2010.02.054

DO - 10.1016/j.amc.2010.02.054

M3 - Article

VL - 216

SP - 3439

EP - 3449

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 12

ER -