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Zbl 1203.47078
Su, Yongfu; Wang, Dongxing; Shang, Meijuan
(Su, Yong-fu; Wang, Dong-xing; Shang, Mei-juan)
Strong convergence of monotone hybrid algorithm for hemi-relatively nonexpansive mappings.
(English)
[J] Fixed Point Theory Appl. 2008, Article ID 284613, 8 p. (2008). ISSN 1687-1812/e

Summary: The purpose of this article is to prove strong convergence theorems for fixed points of closed hemi-relatively nonexpansive mappings. In order to get these convergence theorems, the monotone hybrid iteration method is presented and is used to approximate those fixed points. Note that the hybrid iteration method presented by {\it S.\,Matsushita} and {\it W.\,Takahashi} [J.~Approximation Theory 134, No.\,2, 257--266 (2005; Zbl 1071.47063)] can be used for relatively nonexpansive mapping, but it cannot be used for hemi-relatively nonexpansive mapping. The results of this paper modify and improve the results of {\it S.\,Matsushita} and {\it W.\,Takahashi} [op.\,cit.] and some others.
MSC 2000:
*47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties

Citations: Zbl 1071.47063

Cited in: Zbl 1203.47091

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