2010 Fiscal Year Final Research Report
On error bounds for fixed point problems and its applications
| Project/Area Number |
20740084
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Akita Prefectural University (2009-2010)
Matsue National College of Technology (2008) |
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Principal Investigator |
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| Project Period (FY) |
2008 – 2010
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| Keywords | 不動点問題 / エラーバウンド / 近接点法 |
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| Research Abstract |
This research aims to develop efficient algorithms for solving fixed point problems. Especially, we investigated notions that guarantee sequences generated by iterative methods can obtain an exact solution in finite number of steps. First, we provided a new condition for set-valued mappings based on theoretical techniques for solving the convex programming problem. Further, by using these results, we derived finite convergence results concerning nonlinear problems such as the convex minimization problem and the variational inequality.
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