A sufficient and necessary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings
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Abstract:
In this paper, we prove a Halpern-type strong convergence theorem for nonexpansive mappings in a Banach space whose norm is uniformly Gâteaux differentiable. Also, we discuss the sufficient and necessary condition about this theorem. This is a partial answer of the problem raised by Reich in 1983.References
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Additional Information
- Tomonari Suzuki
- Affiliation: Department of Mathematics, Kyushu Institute of Technology, Sensuicho, Tobata, Kitakyushu 804-8550, Japan
- Email: suzuki-t@mns.kyutech.ac.jp
- Received by editor(s): March 1, 2005
- Received by editor(s) in revised form: July 18, 2005
- Published electronically: June 13, 2006
- Additional Notes: The author was supported in part by Grants-in-Aid for Scientific Research from the Japanese Ministry of Education, Culture, Sports, Science and Technology.
- Communicated by: Joseph A. Ball
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 99-106
- MSC (2000): Primary 47H09; Secondary 47H10
- DOI: https://doi.org/10.1090/S0002-9939-06-08435-8
- MathSciNet review: 2280199