2013 Fiscal Year Final Research Report
Nonlinear analysis using the technique of set-valued analysis
| Project/Area Number |
22540175
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Toho University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
AOYAMA Koji 千葉大学, 法経学部, 教授 (20293152)
IIDUKA Hideaki 明治大学, 理工学部, 准教授 (50532280)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 不動点問題 / 変分不等式 / 均衡問題 / 近似列 / 測地距離空間 |
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| Research Abstract |
In this research, we deal with some nonlinear problems including fixed point problems and equilibrium problems, which are strongly connected to convex analysis, and consider the existence and approximation of the solutions to these problems. We focus our interest in the class of mappings which includes the resolvents of monotone operators and nonexpansive mappings and obtain some results concerning the relation between the boundedness of approximate sequences and the existence of the solution, and the convergence properties of the iterative schemes.
We also consider the iterative schemes of the operators defined on complete geodesic spaces. In particular, we obtain several considerable results for the space having a curvature bounded above by a positive number. Further we obtain some important results about the convergence properties of the schemes with errors related to the computer simulation.
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