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Journal of Applied Mathematics and Computing

, Volume 34, Issue 1–2, pp 407–439 | Cite as

A general iterative method for solving equilibrium problems, variational inequality problems and fixed point problems of an infinite family of nonexpansive mappings

  • Chaichana Jaiboon
  • Poom Kumam
Article

Abstract

In this paper, we introduce and analyze a new general iterative scheme by the viscosity approximation method for finding the common element of the set of equilibrium problems, the set of fixed points of an infinite family of nonexpansive mappings and the set solutions of the variational inequality problems for an ξ-inverse-strongly monotone mapping in Hilbert spaces. We show that the sequence converge strongly to a common element of the above three sets under some parameters controlling conditions. The result extends and improves a recent result of Chang et al. (Nonlinear Anal. 70:3307–3319, 2009) and many others.

Keywords

Nonexpansive mapping ξ-inverse-strongly monotone mapping Variational inequality problem Equilibrium problem Fixed points 

Mathematics Subject Classification (2000)

46C05 47H09 47H10 

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Copyright information

© Thai Government  2009

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceKing Mongkut’s University of Technology ThonburiBangkokThailand

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