Let H be a real Hilbert space. Suppose that T is a nonexpansive mapping on H with a fixed point, f is a contraction on H with coefficient 0 < ฮฑ < 1, and 2 )/ฮฑ = ฯ /ฮฑ. We proved that the sequence {x n } generated by the iterative method )Tx n converges strongly to a fixed point x โ F ix (T ), which
Convergence of a general iterative method for nonexpansive mappings in Hilbert spaces
โ Scribed by Yeol Je Cho; Xiaolong Qin
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 481 KB
- Volume
- 228
- Category
- Article
- ISSN
- 0377-0427
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โฆ Synopsis
In this paper, we introduce a modified Ishikawa iterative process for approximating a fixed point of nonexpansive mappings in Hilbert spaces. We establish some strong convergence theorems of the general iteration scheme under some mild conditions. The results improve and extend the corresponding results of many others.
๐ SIMILAR VOLUMES
We study the approximation of common fixed points of a finite family of nonexpansive mappings and suggest a modification of the iterative algorithm without the assumption of any type of commutativity. Also we show that the convergence of the proposed algorithm can be proved under some types of contr
In this paper, we introduce a new iterative method of a k-strictly pseudo-contractive mapping for some 0 โค k < 1 and prove that the sequence {x n } converges strongly to a fixed point of T , which solves a variational inequality related to the linear operator A. Our results have extended and improve