Mathematical Methods of Operations Research

, Volume 67, Issue 3, pp 375–390 | Cite as

Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities

Original Article

Abstract

In this paper, we introduce and study a relaxed extragradient method for finding solutions of a general system of variational inequalities with inverse-strongly monotone mappings in a real Hilbert space. First, this system of variational inequalities is proven to be equivalent to a fixed point problem of nonexpansive mapping. Second, by using the demi-closedness principle for nonexpansive mappings, we prove that under quite mild conditions the iterative sequence defined by the relaxed extragradient method converges strongly to a solution of this system of variational inequalities. In addition, utilizing this result, we provide some applications of the considered problem not just giving a pure extension of existing mathematical problems.

Keywords

Nonexpansive mapping Common fixed point Demi-closedness principle Inverse-strongly monotone mapping General system of variational inequalities 

Mathematics Subject Classification (2000)

49J30 49J40 47H05 47H10 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Normal UniversityShanghaiChina
  2. 2.Institute of Operations ResearchQufu Normal UniversityQufu, ShandongChina
  3. 3.Department of Applied MathematicsNational Sun Yat-Sen UniversityKaohsiungTaiwan

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