Fixed point theorems for nonlinear non-self mappings in Hilbert spaces and applications

Wataru Takahashi Ngai-Ching Wong Jen-Chih Yao

Functional Analysis mathscidoc:1910.43700

Fixed Point Theory and Applications, 2013, (1), 116, 2013.12
Recently, Kawasaki and Takahashi (J. Nonlinear Convex Anal. 14:71-87, 2013) defined a broad class of nonlinear mappings, called widely more generalized hybrid, in a Hilbert space which contains generalized hybrid mappings (Kocourek <i>et al.</i> in Taiwan. J.Math. 14:2497-2511, 2010) and strict pseudo-contractive mappings (Browder and Petryshyn in J. Math. Anal. Appl. 20:197-228, 1967). They proved fixed point theorems for such mappings. In this paper, we prove fixed point theorems for widely more generalized hybrid non-self mappings in a Hilbert space by using the idea of Hojo <i>et al.</i> (Fixed Point Theory 12:113-126, 2011) and Kawasaki and Takahashi fixed point theorems (J.Nonlinear Convex Anal. 14:71-87, 2013). Using these fixed point theorems for non-self mappings, we proved the Browder and Petryshyn fixed point theorem (J.Math. Anal. Appl. 20:197-228, 1967) for strict pseudo-contractive
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@inproceedings{wataru2013fixed,
  title={Fixed point theorems for nonlinear non-self mappings in Hilbert spaces and applications},
  author={Wataru Takahashi, Ngai-Ching Wong, and Jen-Chih Yao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020211142737067229},
  booktitle={Fixed Point Theory and Applications},
  volume={2013},
  number={1},
  pages={116},
  year={2013},
}
Wataru Takahashi, Ngai-Ching Wong, and Jen-Chih Yao. Fixed point theorems for nonlinear non-self mappings in Hilbert spaces and applications. 2013. Vol. 2013. In Fixed Point Theory and Applications. pp.116. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020211142737067229.
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