### Abstract

Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let A_{i}: C → H, for i = 1, 2; be two L_{i}-Lipschitz monotone mappings and let f: C → C be a contraction mapping. It is our purpose in this paper to introduce an iterative process for finding a point in V I(C,A_{1}) ∩ V I(C, A_{2}) under appropriate conditions. As a consequence, we obtain a convergence theorem for approximating a common solution of a finite family of variational inequality problems for Lipschitz monotone mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

Original language | English |
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Pages (from-to) | 1645-1657 |

Number of pages | 13 |

Journal | Journal of Nonlinear Science and Applications |

Volume | 9 |

Issue number | 4 |

Publication status | Published - Jan 1 2016 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Algebra and Number Theory

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## Cite this

Alghamdi, M. A., Shahzad, N., & Zegeye, H. (2016). Construction of a common solution of a finite family of variational inequality problems for monotone mappings.

*Journal of Nonlinear Science and Applications*,*9*(4), 1645-1657.