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On Reich’s strong convergence theorem for asymptotically nonexpansive mappings in Banach spaces

✍ Scribed by S.S. Chang; H.W. Joseph Lee; Chi Kin Chan

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
185 KB
Volume
66
Category
Article
ISSN
0362-546X

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✦ Synopsis

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.

📜 SIMILAR VOLUMES

Strong Convergence of Averaged Approxima
Strong Convergence of Averaged Approximants for Asymptotically Nonexpansive Mappings in Banach Spaces
✍ Naoki Shioji; Wataru Takahashi 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 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