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Zbl 1189.47071
Yao, Yonghong; Chen, Rudong; Yao, Jen-Chih
(Yao, Yong-hong; Chen, Ru-dong)
Strong convergence and certain control conditions for modified Mann iteration. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 68, No. 6, A, 1687-1693 (2008). ISSN 0362-546X

In this paper, the authors propose a new modified Mann iteration for computing fixed points of nonexpansive mappings in a Banach space setting. This new iterative scheme combines the modified Mann iteration introduced by {\it T.\,H.\thinspace Kim} and {\it H.\,K.\thinspace Xu} [``Strong convergence of modified Mann iterations", Nonlinear Anal., Theory Methods Appl.\ 61, No.\,1--2 (A), 51--60 (2005; Zbl 1091.47055)] and the viscosity approximation method introduced by {\it A.\,Moudafi} [``Viscosity approximation methods for fixed-points problems", J.~Math.\ Anal.\ Appl.\ 241, No.\,1, 46--55 (2000; Zbl 0957.47039)]. The main results extend and improve some due to Xu and Kim in the aforementioned paper.
[Zhilin Yang (Qingdao)]

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: strong convergence; modified Mann iteration; nonexpansive mapping; uniformly smooth Banach space; fixed point

Citations: Zbl 1091.47055; Zbl 0957.47039

Cited in: Zbl 1229.47106 Zbl 1203.47072

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