The purpose of this paper is to establish some necessary and sufficient conditions for the strong convergence of the Ishikawa iterative sequence and the Mann iterative sequence to a fixed point of pseudocontractive mapping in Banach spaces. Our results, to some extent, improve and extend the well-kn
โฆ LIBER โฆ
A necessary and sufficient condition for the strong convergence of nonexpansive mappings in Banach spaces
โ Scribed by Wang, Shuang; Qian, Dingbian
- Book ID
- 125401644
- Publisher
- Springer International Publishing AG
- Year
- 2014
- Tongue
- English
- Weight
- 211 KB
- Volume
- 2014
- Category
- Article
- ISSN
- 1687-1820
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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