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Vietnam Journal of Mathematics

, Volume 44, Issue 2, pp 351–374 | Cite as

Parallel Hybrid Iterative Methods for Variational Inequalities, Equilibrium Problems, and Common Fixed Point Problems

  • Pham Ky Anh
  • Dang Van Hieu
Article

Abstract

In this paper, we propose two strongly convergent parallel hybrid iterative methods for finding a common element of the set of fixed points of a family of asymptotically quasi ϕ-nonexpansive mappings, the set of solutions of variational inequalities and the set of solutions of equilibrium problems in uniformly smooth and 2-uniformly convex Banach spaces. A numerical experiment is given to verify the efficiency of the proposed parallel algorithms.

Keywords

Asymptotically quasi ϕ-nonexpansive mapping Variational inequality Equilibrium problem Hybrid method Parallel computation 

Mathematics Subject Classification (2010)

47H05 47H09 47H10 47J25 65J15 65Y05 

Notes

Acknowledgments

The research of the first author was partially supported by Vietnam Institute for Advanced Study in Mathematics (VIASM) and Vietnam National Foundation for Science and Technology Development (NAFOSTED).

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  1. 1.Hanoi University of Science, Vietnam National UniversityHanoiVietnam

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