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Vietnam Journal of Mathematics

, Volume 43, Issue 1, pp 71–91 | Cite as

A Fixed Point Scheme for Nonexpansive Mappings, Variational Inequalities and Equilibrium Problems

  • Pham N. Anh
  • Le Q. Thuy
  • Do D. Thanh
Article

Abstract

The purpose of this paper is to introduce a new iteration scheme and prove a strong convergence theorem for finding a common element of the fixed point set of a nonexpansive mapping, the solution set of variational inequalities and the solution set of equilibrium problems. Under certain conditions on parameters, we show that the iterative sequences generated by the scheme strongly converge to a common element in a real Hilbert space.

Keywords

Nonexpansive Pseudomonotone Continuous Fixed point Variational inequalities Equilibrium problems 

Mathematics Subject Classification (2000)

65K10 90C33 

Notes

Acknowledgements

This work is supported by the Vietnam Institute for Advanced Study in Mathematics.

We are very grateful to two anonymous referees for their really helpful and constructive comments on improving the paper.

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2014

Authors and Affiliations

  1. 1.Department of Scientific FundamentalsPosts and Telecommunications Institute of TechnologyHanoiVietnam
  2. 2.School of Applied Mathematics and InformaticsHa Noi University of Science and TechnologyHai Ba TrungVietnam
  3. 3.Department of MathematicsHaiphong UniversityHaiphongVietnam

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