Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems

Lu-Chuan Ceng Nicolas Hadjisavvas Ngai-Ching Wong

Functional Analysis mathscidoc:1910.43625

Journal of Global Optimization, 46, (4), 635-646, 2010.4
The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points <i>F</i>(<i>S</i>) of a nonexpansive mapping <i>S</i> and the set of solutions <sub> <i>A</i> </sub> of the variational inequality for a monotone, Lipschitz continuous mapping <i>A</i>. We introduce a hybrid extragradient-like approximation method which is based on the well-known extragradient method and a hybrid (or outer approximation) method. The method produces three sequences which are shown to converge strongly to the same common element of {F(S)\cap\Omega_{A}}. As applications, the method provides an algorithm for finding the common fixed point of a nonexpansive mapping and a pseudocontractive mapping, or a common zero of a monotone Lipschitz continuous mapping and a maximal monotone mapping.
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@inproceedings{lu-chuan2010strong,
  title={Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems},
  author={Lu-Chuan Ceng, Nicolas Hadjisavvas, and Ngai-Ching Wong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020204639163596154},
  booktitle={Journal of Global Optimization},
  volume={46},
  number={4},
  pages={635-646},
  year={2010},
}
Lu-Chuan Ceng, Nicolas Hadjisavvas, and Ngai-Ching Wong. Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems. 2010. Vol. 46. In Journal of Global Optimization. pp.635-646. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020204639163596154.
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