### 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 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Algebra and Number Theory

### Cite this

*Journal of Nonlinear Science and Applications*,

*9*(4), 1645-1657.

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*Journal of Nonlinear Science and Applications*, vol. 9, no. 4, pp. 1645-1657.

**Construction of a common solution of a finite family of variational inequality problems for monotone mappings.** / Alghamdi, Mohammed Ali; Shahzad, Naseer; Zegeye, Habtu.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Construction of a common solution of a finite family of variational inequality problems for monotone mappings

AU - Alghamdi, Mohammed Ali

AU - Shahzad, Naseer

AU - Zegeye, Habtu

PY - 2016/1/1

Y1 - 2016/1/1

N2 - Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let Ai: C → H, for i = 1, 2; be two Li-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,A1) ∩ V I(C, A2) 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.

AB - Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let Ai: C → H, for i = 1, 2; be two Li-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,A1) ∩ V I(C, A2) 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.

UR - http://www.scopus.com/inward/record.url?scp=84955618962&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84955618962&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84955618962

VL - 9

SP - 1645

EP - 1657

JO - Journal of Nonlinear Science and Applications

JF - Journal of Nonlinear Science and Applications

SN - 2008-1898

IS - 4

ER -