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Strong convergence theorems for semigroups of asymptotically nonexpansive mappings in Banach spaces

DR Sahu Ngai-Ching Wong Jen-Chih Yao

Functional Analysis mathscidoc:1910.43715

Abstract and Applied Analysis, 2013, 2013
Let be a real reflexive Banach space with a weakly continuous duality mapping . Let be a nonempty weakly closed star-shaped (with respect to ) subset of . Let = be a uniformly continuous semigroup of asymptotically nonexpansive self-mappings of , which is uniformly continuous at zero. We will show that the implicit iteration scheme: , for all , converges strongly to a common fixed point of the semigroup for some suitably chosen parameters and . Our results extend and improve corresponding ones of Suzuki (2002), Xu (2005), and Zegeye and Shahzad (2009).
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@inproceedings{dr2013strong,
  title={Strong convergence theorems for semigroups of asymptotically nonexpansive mappings in Banach spaces},
  author={DR Sahu, Ngai-Ching Wong, and Jen-Chih Yao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020211617706622244},
  booktitle={Abstract and Applied Analysis},
  volume={2013},
  year={2013},
}
DR Sahu, Ngai-Ching Wong, and Jen-Chih Yao. Strong convergence theorems for semigroups of asymptotically nonexpansive mappings in Banach spaces. 2013. Vol. 2013. In Abstract and Applied Analysis. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020211617706622244.
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