Strong and weak convergence theorems for an infinite family of nonexpansive mappings and applications

Lu-Chuan Ceng Ngai-Ching Wong Jen-Chih Yao

Functional Analysis mathscidoc:1910.43674

Fixed Point Theory and Applications, 2012, (1), 117, 2012.12
In this paper, let E be a reflexive and strictly convex Banach space which either is uniformly smooth or has a weakly continuous duality map. We consider the hybrid viscosity approximation method for finding a common fixed point of an infinite family of nonexpansive mappings in E. We prove the strong convergence of this method to a common fixed point of the infinite family of nonexpansive mappings, which solves a variational inequality on their common fixed point set. We also give a weak convergence theorem for the hybrid viscosity approximation method involving an infinite family of nonexpansive mappings in a Hilbert space. MSC:47H17, 47H09, 47H10, 47H05.
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@inproceedings{lu-chuan2012strong,
  title={Strong and weak convergence theorems for an infinite family of nonexpansive mappings and applications},
  author={Lu-Chuan Ceng, Ngai-Ching Wong, and Jen-Chih Yao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020210252350388203},
  booktitle={Fixed Point Theory and Applications},
  volume={2012},
  number={1},
  pages={117},
  year={2012},
}
Lu-Chuan Ceng, Ngai-Ching Wong, and Jen-Chih Yao. Strong and weak convergence theorems for an infinite family of nonexpansive mappings and applications. 2012. Vol. 2012. In Fixed Point Theory and Applications. pp.117. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020210252350388203.
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