Weak Convergence of an Iterative Method for Pseudomonotone Variational Inequalities and Fixed-Point Problems

Article

Abstract

We consider an iterative scheme for finding a common element of the set of solutions of a pseudomonotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of N nonexpansive mappings. The proposed iterative method combines two well-known schemes: extragradient and approximate proximal methods. We derive a necessary and sufficient condition for weak convergence of the sequences generated by the proposed scheme.

Keywords

Variational inequalities Nonexpansive mappings Extragradient methods Approximate proximal methods Pseudomonotone mappings Fixed points Weak convergence Opial condition 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Normal UniversityShanghaiChina
  2. 2.Scientific Computing Key Laboratory of Shanghai UniversitiesShanghaiChina
  3. 3.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael
  4. 4.Department of Applied MathematicsNational Sun Yat-sen UniversityKaohsiungRepublic of China

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