EXTRAGRADIENT METHOD FOR EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITIES

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/j.na.2008.02.014] as a special case.