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Attractive points and Halpern-type strong convergence theorems in Hilbert spaces

Wataru Takahashi Ngai-Ching Wong Jen-Chih Yao

Functional Analysis mathscidoc:1910.43722

Journal of Fixed Point Theory and Applications, 17, (2), 301-311, 2015.6
In this paper, using the concept of attractive points of a nonlinear mapping, we obtain a strong convergence theorem of Halperns type [<i>Bull. Amer. Math. Soc</i>. <b>73</b> (1967), 957961] for a wide class of nonlinear mappings which contains nonexpansive mappings, nonspreading mappings and hybrid mappings in a Hilbert space. Using this result, we obtain well-known and new strong convergence theorems of Halperns type in a Hilbert space. In particular, we solve a problem posed by Kurokawa and Takahashi [<i>Nonlinear Anal</i>. <b>73</b> (2010, 15621568].
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@inproceedings{wataru2015attractive,
  title={Attractive points and Halpern-type strong convergence theorems in Hilbert spaces},
  author={Wataru Takahashi, Ngai-Ching Wong, and Jen-Chih Yao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020211930683975251},
  booktitle={Journal of Fixed Point Theory and Applications},
  volume={17},
  number={2},
  pages={301-311},
  year={2015},
}
Wataru Takahashi, Ngai-Ching Wong, and Jen-Chih Yao. Attractive points and Halpern-type strong convergence theorems in Hilbert spaces. 2015. Vol. 17. In Journal of Fixed Point Theory and Applications. pp.301-311. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020211930683975251.
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