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Strong convergence theorems for an infinite family of nonexpansive mappings in Banach spaces

✍ Scribed by Xiaolong Qin; Yeol Je Cho; Jung Im Kang; Shin Min Kang

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
436 KB
Volume
230
Category
Article
ISSN
0377-0427

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✦ Synopsis

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.

πŸ“œ SIMILAR VOLUMES

On Reich’s strong convergence theorem fo
On Reich’s strong convergence theorem for asymptotically nonexpansive mappings in Banach spaces
✍ S.S. Chang; H.W. Joseph Lee; Chi Kin Chan πŸ“‚ Article πŸ“… 2007 πŸ› Elsevier Science 🌐 English βš– 185 KB

The purpose of this paper is to study Reich's strongly convergence theorems for asymptotically nonexpansive mappings in Banach spaces. Under some general conditions an affirmative partial answer to Reich's open question is given and some recent results are improved and generalized.

Strong Convergence of Averaged Approxima
Strong Convergence of Averaged Approximants for Asymptotically Nonexpansive Mappings in Banach Spaces
✍ Naoki Shioji; Wataru Takahashi πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 129 KB

Let C be a closed, convex subset of a uniformly convex Banach space whose norm is uniformly Ga^teaux differentiable and let T be an asymptotically nonexpansive mapping from C into itself such that the set F(T ) of fixed points of T is nonempty. In this paper, we show that F(T ) is a sunny, nonexpans