Strong convergence of the CQ method for fixed point iteration processes
β Scribed by Carlos Martinez-Yanes; Hong-Kun Xu
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 159 KB
- Volume
- 64
- Category
- Article
- ISSN
- 0362-546X
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## Abstract Let __E__ be a real reflexive Banach space having a weakly continuous duality mapping __J__~__Ο__~ with a gauge function __Ο__, and let __K__ be a nonempty closed convex subset of __E__. Suppose that __T__ is a nonβexpansive mapping from __K__ into itself such that __F__ (__T__) β β οΈ.
This paper surveys some of the main convergence properties of the Mann-type iteration for the demicontractive mappings. Some variants of the Mann iteration that ensure the strong convergence, like the (CQ) algorithm and a variant for the asymptotically demicontractive mappings are also considered. T
In this paper, we introduce a modified Mann iterative process for approximating a common fixed point of a finite family of strict pseudo-contractions in Hilbert spaces. We establish the strong convergence theorem of the general iteration scheme under some mild conditions. Our results extend and impr