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 |
Section | 一般 |
Research Field |
Basic analysis
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Research Institution | Toho University |
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)
|
Project Period (FY) |
2010-04-01 – 2014-03-31
|
Project Status |
Completed (Fiscal Year 2013)
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Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
Keywords | 不動点問題 / 変分不等式 / 均衡問題 / 近似列 / 測地距離空間 / 非線形問題 / 不動点 / 凸解析 |
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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Report
(5 results)
Research Products
(78 results)
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[Presentation] 写像列の強非拡大性2010
Author(s)
青山耕治
Organizer
日本数学会2010年度秋季総合分科会
Place of Presentation
名古屋大学(愛知県)
Year and Date
2010-09-24
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