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Acta Mathematica Vietnamica

, Volume 43, Issue 2, pp 239–255 | Cite as

A New Simple Parallel Iteration Method for a Class of Variational Inequalities

  • Nguyen Song Song Ha
  • Nguyen Buong
  • Nguyen Thi Thu Thuy
Article
  • 63 Downloads

Abstract

In this paper, we propose a new simple parallel iterative method to find a solution for variational inequalities over the set of common fixed points of an infinite family of nonexpansive mappings on real reflexive and strictly convex Banach spaces with a uniformly Gâteaux differentiable norm. Our parallel iterative method is simpler than the one proposed by Buong et al. (Numer. Algorithms 72, 467–481 2016). An iterative method of Halpern type for common zeros of an infinite family of m-accretive mappings is shown as a special case of our result. Two numerical examples are also given to illustrate the effectiveness and superiority of the proposed algorithm.

Keywords

Fixed point Nonexpansive and accretive mapping Variational inequality Common zero of accretive mappings Iterative algorithms 

Mathematics Subject Classification (2010)

47J05 47H09 49J30 

Notes

Acknowledgements

The authors are extremely grateful to Prof. Nguyen Tu Cuong and the referees for many helpful comments and suggestions, which helped to improve this paper.

Funding Information

This work was supported by the Vietnam National Foundation for Science and Technology Development under the code 101.02-2017.305.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  • Nguyen Song Song Ha
    • 1
  • Nguyen Buong
    • 2
  • Nguyen Thi Thu Thuy
    • 1
  1. 1.Thainguyen College of SciencesThainguyen UniversityThai NguyenVietnam
  2. 2.Institute of Information TechnologyVietnam Academy of Science and TechnologyHanoiVietnam

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