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An Extragradient Method for Fixed Point Problems and Variational Inequality Problems

Abstract

We present an extragradient method for fixed point problems and variational inequality problems. Using this method, we can find the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for monotone mapping.

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Correspondence to Yonghong Yao.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Yao, Y., Liou, YC. & Yao, JC. An Extragradient Method for Fixed Point Problems and Variational Inequality Problems. J Inequal Appl 2007, 038752 (2007). https://doi.org/10.1155/2007/38752

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Keywords

  • Variational Inequality
  • Monotone Mapping
  • Nonexpansive Mapping
  • Common Element
  • Point Problem
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