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Iterative methods for the computation of fixed points of demicontractive mappings

✍ Scribed by Charles E. Chidume; Ştefan Măruşter

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
570 KB
Volume
234
Category
Article
ISSN
0377-0427

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✦ Synopsis

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. The usual framework of our study is a (real) Hilbert space and only to a certain extent some particular Banach spaces. Historical aspects are pointed out and some applications for the convex feasibility problem are discussed.

📜 SIMILAR VOLUMES

Iterative methods for common fixed point
Iterative methods for common fixed points for a countable family of nonexpansive mappings in uniformly convex spaces
✍ C.E. Chidume; C.O. Chidume 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 679 KB

Let E be a uniformly convex real Banach space with a uniformly Gâteaux differentiable norm. Let K be a closed, convex and nonempty subset of E. Let {T i } ∞ i=1 be a family of nonexpansive self-mappings of K . For arbitrary fixed δ ∈ (0, 1), define a family of nonexpansive maps , where {α n } and {