CONVERGENCE ANALYSIS OF A HYBRID RELAXED-EXTRAGRADIENT METHOD FOR MONOTONE VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS
Lu-Chuan Ceng, B. T. Kien, Ngai‐Ching Wong · 2008
Abstract. In this paper we introduce a hybrid relaxed-extragradient method for finding a common element of the set of common fixed points of N nonexpansive mappings and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The hybrid relaxed-extragradient method is based on two well-known methods: hybrid and extragradient. We derive a strong convergence theorem for three sequences generated by this method. Based on this theorem, we also construct an iterative process for finding a common fixed point of N+1 mappings, such that one of these mappings is taken from the more general class of Lipschitz pseudocontractive mappings and the rest N mappings are nonexpansive. Key words. Variational inequality, nonexpansive mapping, extragradient method, hybrid