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Zbl 1170.47043
Qin, Xiaolong; Cho, Yeol Je; Kang, Jung Im; Kang, Shin Min
(Qin, Xiao-long)
Strong convergence theorems for an infinite family of nonexpansive mappings in Banach spaces. (English)
[J] J. Comput. Appl. Math. 230, No. 1, 121-127 (2009). ISSN 0377-0427

Summary: In an infinite-dimensional Hilbert space, the normal Mann's iteration algorithm has only weak convergence, in general, even for nonexpansive mappings. In order to get a strong convergence result, we modify the normal Mann's iterative process for an infinite family of nonexpansive mappings in the framework of Banach spaces. Our results improve and extend the recent results announced by many others.
[Jiří Vaníček (Praha)]

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: fixed point problem in Banach space; nonexpansive mapping; contraction; Mann's iteration

Cited in: Zbl 1189.65116

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