Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings

N. Nadezhkina and W. Takahashi
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N. Nadezhkina: Tokyo Institute of Technology
W. Takahashi: Tokyo Institute of Technology

Journal of Optimization Theory and Applications, 2006, vol. 128, issue 1, No 9, 201 pages

Abstract: 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 (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (21)

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DOI: 10.1007/s10957-005-7564-z

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