Consider the variational inequality (VI)
x* ∈C, ‹Fx*, x - x* ›≥0, x∈C (*)
where C is a nonempty closed convex subset of a real Hilbert space H and
F : C¡÷ H is a monotone operator form C into H. It is known that if F is
strongly monotone and Lipschitzian, then VI (*) is equivalently turned into
a fixed point problem of a contraction; hence Banach's contraction principle
applies. However, in the case where F is inverse strongly monotone, VI (*)
is equivalently transformed into a fixed point problem of a nonexpansive
mapping. The purpose of this paper is to present some results which apply
iterative methods for nonexpansive mappings to solve VI (*). We introduce
Mann's algorithm and Halpern's algorithm and prove that the sequences
generated by these algorithms converge weakly and respectively, strongly to
a solution of VI (*), under appropriate conditions imposed on the parameter
sequences in the algorithms.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0626110-101550 |
| Date | 26 June 2010 |
| Creators | Lin, Yen-Ru |
| Contributors | Lai-Jiu Lin, Hong-Kun Xu, Jen-Chih Yao, 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-0626110-101550 |
| Rights | withheld, Copyright information available at source archive |
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