Some Modified Extragradient Approximation Methods for Variational Inequality Problems and Equilibrium Problems of Nonexpansive Mappings 1
Rabian Wangkeeree, Uthai Kamraksa · 2009
Abstract. In this paper, we introduce a modified extragradient approximation method for finding the common element of the set of fixed points of nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling con-ditions. Our results extend and improve a recent result of Bnouhachem, Aslam Noor, and Hao [2] [A. Bnouhachem, M. Aslam Noor and Z. Hao, Some new extra-gradient iterative methods for variational inequalities, Nonlinear Analysis (2008), doi:10.1016/j.na.2008.02.014] and many other.