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Zbl 1206.47088
Su, Yongfu; Wang, Ziming; Xu, Hongkun
(Su, Yong-fu; Wang, Zi-ming; Xu, Hong-kun)
Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings.
(English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 11, A, 5616-5628 (2009). ISSN 0362-546X

Summary: The purpose of this article is to prove strong convergence theorems for common fixed points of two closed hemi-relatively nonexpansive mappings in Banach spaces. In order to get the strong convergence theorems, monotone hybrid algorithms are presented and are used to approximate the common fixed points. Finally, a new simplified hybrid algorithm is proposed and a relative convergence theorem is proved by using a new method for the proofs. The results of this article modify and improve the results of {\it S.-Y.\thinspace Matsushita} and {\it W.\,Takahashi} [J.~Approximation Theory 134, No.\,2, 257--266 (2005; Zbl 1071.47063)], {\it S.\,Plubtieng} and {\it K.\,Ungchittrakool} [J.~Approximation Theory 149, No.\,2, 103--115 (2007; Zbl 1137.47056)] and many others.
MSC 2000:
*47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties

Keywords: relatively nonexpansive mapping; hemi-relatively nonexpansive mapping; generalized projection; common fixed point; monotone hybrid algorithm

Citations: Zbl 1071.47063; Zbl 1137.47056

Cited in: Zbl 1215.47091 Zbl 1207.47074

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