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A new hybrid iterative method for solution of equilibrium problems and fixed point problems for an inverse strongly monotone operator and a nonexpansive mapping

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Abstract

In this paper, we introduce an iterative scheme by a new hybrid method for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in a real Hilbert space. We show that the iterative sequence converges strongly to a common element of the above three sets under some parametric controlling conditions by the new hybrid method which is introduced by Takahashi et al. (J. Math. Anal. Appl., doi: 10.1016/j.jmaa.2007.09.062, 2007). The results are connected with Tada and Takahashi’s result [A. Tada and W. Takahashi, Weak and strong convergence theorems for a nonexpansive mappings and an equilibrium problem, J. Optim. Theory Appl. 133, 359–370, 2007]. Moreover, our result is applicable to a wide class of mappings.

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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

    Poom Kumam

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  1. Poom Kumam
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Correspondence to Poom Kumam.

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This work was completed with the support of the Thailand Research Fund and the Commission on Higher Education under project no. MRG5180034.

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Kumam, P. A new hybrid iterative method for solution of equilibrium problems and fixed point problems for an inverse strongly monotone operator and a nonexpansive mapping. J. Appl. Math. Comput. 29, 263–280 (2009). https://doi.org/10.1007/s12190-008-0129-1

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  • DOI: https://doi.org/10.1007/s12190-008-0129-1

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