Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings Authors N. Nadezhkina Department of Mathematical and Computing Sciences Tokyo Institute of Technology W. Takahashi Department of Mathematical and Computing Sciences Tokyo Institute of Technology Article

DOI :
10.1007/s10957-005-7564-z

Cite this article as: Nadezhkina, N. & Takahashi, W. J Optim Theory Appl (2006) 128: 191. doi:10.1007/s10957-005-7564-z
Abstract 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

Keywords Extragradient method fixed points monotone mappings nonexpansive mappings variational inequalities Communicated by S. Schaible

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