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A generalized hybrid steepest-descent method for variational inequalities in Banach spaces

DR Sahu Ngai-Ching Wong Jen-Chih Yao

Functional Analysis mathscidoc:1910.43639

Fixed Point Theory and Applications, 2011, (1), 754702, 2011.12
The hybrid steepest-descent method introduced by Yamada (2001) is an algorithmic solution to the variational inequality problem over the fixed point set of nonlinear mapping and applicable to a broad range of convexly constrained nonlinear inverse problems in real Hilbert spaces. Lehdili and Moudafi (1996) introduced the new prox-Tikhonov regularization method for proximal point algorithm to generate a strongly convergent sequence and established a convergence property for it by using the technique of variational distance in Hilbert spaces. In this paper, motivated by Yamada's hybrid steepest-descent and Lehdili and Moudafi's algorithms, a generalized hybrid steepest-descent algorithm for computing the solutions of the variational inequality problem over the common fixed point set of sequence of nonexpansive-type mappings in the framework of Banach space is proposed. The strong convergence
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@inproceedings{dr2011a,
  title={A generalized hybrid steepest-descent method for variational inequalities in Banach spaces},
  author={DR Sahu, Ngai-Ching Wong, and Jen-Chih Yao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020205153837115168},
  booktitle={Fixed Point Theory and Applications},
  volume={2011},
  number={1},
  pages={754702},
  year={2011},
}
DR Sahu, Ngai-Ching Wong, and Jen-Chih Yao. A generalized hybrid steepest-descent method for variational inequalities in Banach spaces. 2011. Vol. 2011. In Fixed Point Theory and Applications. pp.754702. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020205153837115168.
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