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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok, 10140, Thailand

    Chaichana Jaiboon & Poom Kumam

Authors
  1. Chaichana Jaiboon
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  2. Poom Kumam
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Correspondence to Poom Kumam.

Additional information

This research was partially supported by The Commission on Higher Education under the project: “Fixed Point Theorem in Banach spaces and Metric spaces” Ministry of Education and Faculty of Science, King Mongkut’s University of Technology Thonburi.

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Jaiboon, C., Kumam, P. A general iterative method for solving equilibrium problems, variational inequality problems and fixed point problems of an infinite family of nonexpansive mappings. J. Appl. Math. Comput. 34, 407–439 (2010). https://doi.org/10.1007/s12190-009-0330-x

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  • DOI: https://doi.org/10.1007/s12190-009-0330-x

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