Nadezhkina, N.; Takahashi, W. Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings. (English) Zbl 1130.90055 J. Optim. Theory Appl. 128, No. 1, 191-201 (2006). Summary: In this paper, we introduce an iterative process for finding the 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. The iterative process is based on the so-called extragradient method. We obtain a weak convergence theorem for two sequences generated by this process Cited in 10 ReviewsCited in 231 Documents MSC: 90C52 Methods of reduced gradient type 49J40 Variational inequalities Keywords:Extragradient method; fixed points; monotone mappings; nonexpansive mappings; variational inequalities PDF BibTeX XML Cite \textit{N. Nadezhkina} and \textit{W. Takahashi}, J. Optim. Theory Appl. 128, No. 1, 191--201 (2006; Zbl 1130.90055) Full Text: DOI OpenURL References: [9] Yamada I. The Hybrid Steepest-Descent Method for the Variational Inequality Problem over the Intersection of Fixed-Point Sets of Nonexpansive Mappings, Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, Edited by D. Butnariu, Y. Censor, and S. Reich, Kluwer Academic Publishers, Dordrecht, Netherlands, pp. 473–504, 2001. · Zbl 1013.49005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.