A sequence fxng generates by the formula
x_{n+1} =(1- £\\_n)x_n+ £\\_nT_nx_n is called the Krasnosel'skii-Mann algorithm, where {£\\_n} is a sequence in (0,1) and {T_n} is a sequence of nonexpansive mappings. We introduce KM algorithm and prove that the sequence fxng generated by KM algorithm converges weakly. This result is used to solve the split feasibility problem which is to find a point x with the property that x ∈ C and Ax ∈ Q, where C and Q are closed convex subsets form H1 to H2, respectively, and A is a bounded linear operator form H1 to H2. The purpose of this paper is to present some results which apply KM algorithm to solve the split feasibility problem, the multiple-set split feasibility problem and other applications.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0629110-163913 |
| Date | 29 June 2010 |
| Creators | Liang, Wei-Jie |
| Contributors | Jen-Chih Yao, Hong-Kun Xu, none, Ngai-Ching Wong |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0629110-163913 |
| Rights | not_available, Copyright information available at source archive |
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