Hybrid extragradient method for general equilibrium problems and fixed point problems in Hilbert space |
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Authors: | Issara Inchan |
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Affiliation: | Department of Mathematics and Computer, Faculty of Science and Technology, Uttaradit Rajabhat University, Uttaradit 53000, Thailand |
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Abstract: | In this paper, we introduce an iterative scheme by the hybrid methods for finding a common element of the set of fixed points of nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of a variational inequality problem in a Hilbert space. Then, we prove the strongly convergent theorem by a hybrid extragradient method to the common element of the set of fixed points of nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of a variational inequality problem. Our results extend and improve the results of Bnouhachem et al. [A. Bnouhachem, M. Aslam Noor, Z. Hao, Some new extragradient iterative methods for variational inequalities, Nonlinear Analysis (2008) doi:10.1016/j.na.2008.02.014] and many others. |
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