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A new iterative algorithm of solution for equilibrium problems, variational inequalities and fixed point problems in a Hilbert space

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Abstract

In this paper, we introduce a new iterative method for finding a common element of the set of solutions of an equilibrium problem, the set of solutions of the variational inequality for β-inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in a Hilbert space. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. As applications, at the end of paper we utilize our results to study some convergence problem for finding the zeros of maximal monotone operators. Our results are generalizations and extensions of the results of Yao and Liou (Fixed Point Theory Appl. Article ID 384629, 10 p., 2008), Yao et al. (J. Nonlinear Convex Anal. 9(2):239–248, 2008) and Su and Li (Appl. Math. Comput. 181(1):332–341, 2006) and some recent results.

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Authors and Affiliations

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

    Phayap Katchang & Poom Kumam

Authors
  1. Phayap Katchang
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  2. Poom Kumam
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Correspondence to Poom Kumam.

Additional information

This work was completed with the support of the Commission on Higher Education under the project: “Fixed Point Theory in Banach Spaces and Metric Spaces”, Ministry of Education, Thailand.

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Katchang, P., Kumam, P. A new iterative algorithm of solution for equilibrium problems, variational inequalities and fixed point problems in a Hilbert space. J. Appl. Math. Comput. 32, 19–38 (2010). https://doi.org/10.1007/s12190-009-0230-0

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  • DOI: https://doi.org/10.1007/s12190-009-0230-0

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