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On the Contraction and Nonexpansiveness Properties of the Marginal Mappings in Generalized Variational Inequalities Involving Co-Coercive Operators

  • Pham Ngoc Anh
  • Le Dung Muu
  • Van Hien Nguyen
  • Jean-Jacques Strodiot
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 77)

Abstract

We investigate the contraction and nonexpansiveness properties of the marginal mappings for gap functions in generalized variational inequalities dealing with strongly monotone and co-coercive operators in a real Hilbert space. We show that one can choose regularization operators such that the solution of a strongly monotone variational inequality can be obtained as the fixed point of a certain contractive mapping. Moreover a solution of a co-coercive variational inequality can be computed by finding a fixed point of a certain nonexpansive mapping. The results give a further analysis for some methods based on the auxiliary problem principle. They also lead to new algorithms for solving generalized variational inequalities involving co-coercive operators. By the Banach contraction mapping principle the convergence rate can be easily established.

Keywords

Generalized variational inequality co-coercivity contractive and nonexpansive mapping Banach iterative method 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Pham Ngoc Anh
    • 1
  • Le Dung Muu
    • 2
  • Van Hien Nguyen
    • 3
  • Jean-Jacques Strodiot
    • 3
  1. 1.Posts and TelecommunicationsInstitute of TechnologyVietnam
  2. 2.Hanoi Institute of MathematicsVietnam
  3. 3.Department of MathematicsUniversity of Namur (FUNDP)Belgium

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