Journal of the Chungcheong Mathematical Society (충청수학회지)
- Volume 21 Issue 3
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- Pages.327-337
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- 2008
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- 1226-3524(pISSN)
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- 2383-6245(eISSN)
STRONG CONVERGENCE THEOREM OF FIXED POINT FOR RELATIVELY ASYMPTOTICALLY NONEXPANSIVE MAPPINGS
- Qin, Xiaolong (Department of Mathematics Gyeongsang National University) ;
- Kang, Shin Min (Department of Mathematics and the RINS Gyeongsang National University) ;
- Cho, Sun Young (Department of Mathematics Gyeongsang National University)
- Received : 2008.03.22
- Accepted : 2008.05.05
- Published : 2008.09.30
Abstract
In this paper, we prove strong convergence theorems of Halpern iteration for relatively asymptotically nonexpansive mappings in the framework of Banach spaces. Our results extend and improve the recent ones announced by [C. Martinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006), 2400-2411], [X. Qin, Y. Su, Strong convergence theorem for relatively nonexpansive mappings in a Banach space, Nonlinear Anal. 67 (2007), 1958-1965] and many others.