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Implicit predictor-corrector iteration process for finitely many asymptotically (quasi-) nonexpansive mappings

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

Functional Analysis mathscidoc:1910.43683

Journal of Inequalities and Applications, 2006, (1), 65983, 2006.12
We study an implicit predictor-corrector iteration process for finitely many asymptotically quasi-nonexpansive self-mappings on a nonempty closed convex subset of a Banach space. We derive a necessary and sufficient condition for the strong convergence of this iteration process to a common fixed point of these mappings. In the case is a uniformly convex Banach space and the mappings are asymptotically nonexpansive, we verify the weak (resp., strong) convergence of this iteration process to a common fixed point of these mappings if Opial's condition is satisfied (resp., one of these mappings is semicompact). Our results improve and extend earlier and recent ones in the literature.
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@inproceedings{lu-chuan2006implicit,
  title={Implicit predictor-corrector iteration process for finitely many asymptotically (quasi-) nonexpansive mappings},
  author={Lu-Chuan Ceng, Ngai-Ching Wong, and Jen-Chih Yao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020210523532224212},
  booktitle={Journal of Inequalities and Applications},
  volume={2006},
  number={1},
  pages={65983},
  year={2006},
}
Lu-Chuan Ceng, Ngai-Ching Wong, and Jen-Chih Yao. Implicit predictor-corrector iteration process for finitely many asymptotically (quasi-) nonexpansive mappings. 2006. Vol. 2006. In Journal of Inequalities and Applications. pp.65983. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020210523532224212.
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