Iterative Sequences for Asymptotically Quasi-nonexpansive Mappings
โ Scribed by Liu Qihou
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 65 KB
- Volume
- 259
- Category
- Article
- ISSN
- 0022-247X
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๐ SIMILAR VOLUMES
This paper deals with a necessary and sufficient condition for the convergence of Ishikawa iterates of quasi-nonexpansive mapping in a Banach space. The convergence of Ishikawa iterates for nonexpansive mappings in a uniformly convex Banach space is also discussed.
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
ร 4 ร 4 ร 4 mapping. Given a sequence x in D and two real sequences t and s ร 4 5 5 we prove that if x is bounded, then lim Tx y x s 0. The conditions on n n ยช ฯฑn n D , X, and T are shown which guarantee the weak and strong convergence of the Ishikawa iteration process to a fixed point of T.