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Zbl 1215.47091
Su, Yongfu; Xu, Hong-Kun; Zhang, Xin
(Su, Yong-fu; ;)
Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 12, 3890-3906 (2010). ISSN 0362-546X

Summary: The purpose of this article is to prove strong convergence theorems for common fixed points of two countable families of weak 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. Using this result, we also discuss the problem of strong convergence concerning the maximal monotone operators in a Banach space. The results of this article modify and improve the results of {\it S.-Y. 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)], {\it Y.-F. Su}, {\it Z.-M. Wang} and {\it H.-K. Xu} [Nonlinear Anal., Theory Methods Appl., Ser.~A, Theory Methods 71, No.~11, A, 5616--5628 (2009; Zbl 1206.47088)], and many others.

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties

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

Citations: Zbl 1071.47063; Zbl 1137.47056; Zbl 1206.47088

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