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

Mohammed Ali Alghamdi, Naseer Shahzad, Habtu Zegeye

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1645-1657
Number of pages13
JournalJournal of Nonlinear Science and Applications
Volume9
Issue number4
Publication statusPublished - Jan 1 2016

Fingerprint

Lipschitz Mapping
Monotone Mapping
Variational Inequality Problem
Contraction Mapping
Nonlinear Operator
Iterative Process
Convergence Theorem
Hilbert space
Closed
Subset
Theorem
Family
Class

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory

Cite this

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

In: Journal of Nonlinear Science and Applications, Vol. 9, No. 4, 01.01.2016, p. 1645-1657.

Research output: Contribution to journalArticle

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