A viscosity relaxed-extragradient method for monotone variational inequalities and fixed point problems
Lu-Chuan Ceng, Jen‐Chih Yao · Journal of Mathematical Inequalities · 2007
In this paper we introduce a viscosity relaxed-extragradient method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping in a real Hilbert space H . The viscosity relaxed-extragradient method is based on two methods: extragradientlike approximation method and viscosity approximation method. We derive a weak convergence theorem for two sequences generated by this method. Utilizing this theorem we also construct an iterative process for finding a common zero of two mappings, one of which is a monotone, Lipschitz continuous mapping of H into itself and the other taken from the more general class of maximal monotone mappings of H into 2 H .