Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings |
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| Authors: | N. Nadezhkina W. Takahashi |
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| Affiliation: | (1) Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro, Tokyo, Japan;(2) Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro, Tokyo, Japan |
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| 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 |
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| Keywords: | Extragradient method fixed points monotone mappings nonexpansive mappings variational inequalities |
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