Albanian Journal of Mathematics (ISNN: 1930-1235), Vol 2, No 2 (2008)

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Extragradient method for equilibrium problems and variational inequalities.

Muhammad Aslam Noor, Yonghong Yao, Yeong-Cheng Liou


In this paper, we suggest and analyze a new extragradient
method for finding a common element of the set of
solutions of an equilibrium problem, the set of fixed points of a
nonexpansive mapping and the set of solutions of some variational
inequality. Furthermore, we prove that the proposed iterative
algorithm converges strongly to a common element of the above three sets. Our result includes the main result of Bnouhachem, Noor and Hao [A. Bnouhachem, M.A. Noor and Z. Hao, Some new extragradient methods for variational inequalities, Nonlinear Analysis (2008), doi:10.1016/] as a special case.

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