Necessary and Sufficient Condition for Mann Iteration Converges to a Fixed Point of Lipschitzian Mappings
Joint Authors
Xiang, Chang-He
Zhang, Jiang-Hua
Chen, Zhe
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-09-29
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
Suppose that E is a real normed linear space, C is a nonempty convex subset of E, T:C→C is a Lipschitzian mapping, and x*∈C is a fixed point of T.
For given x0∈C, suppose that the sequence {xn}⊂C is the Mann iterative sequence defined by xn+1=(1-αn)xn+αnTxn,n≥0, where {αn} is a sequence in [0, 1], ∑n=0∞αn2<∞, ∑n=0∞αn=∞.
We prove that the sequence {xn} strongly converges to x* if and only if there exists a strictly increasing function Φ:[0,∞)→[0,∞) with Φ(0)=0 such that limsup n→∞inf j(xn-x*)∈J(xn-x*){〈Txn-x*,j(xn-x*)〉-∥xn-x*∥2+Φ(∥xn-x*∥)}≤0.
American Psychological Association (APA)
Xiang, Chang-He& Zhang, Jiang-Hua& Chen, Zhe. 2012. Necessary and Sufficient Condition for Mann Iteration Converges to a Fixed Point of Lipschitzian Mappings. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-9.
https://search.emarefa.net/detail/BIM-993156
Modern Language Association (MLA)
Xiang, Chang-He…[et al.]. Necessary and Sufficient Condition for Mann Iteration Converges to a Fixed Point of Lipschitzian Mappings. Journal of Applied Mathematics No. 2012 (2012), pp.1-9.
https://search.emarefa.net/detail/BIM-993156
American Medical Association (AMA)
Xiang, Chang-He& Zhang, Jiang-Hua& Chen, Zhe. Necessary and Sufficient Condition for Mann Iteration Converges to a Fixed Point of Lipschitzian Mappings. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-9.
https://search.emarefa.net/detail/BIM-993156
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993156