| Project/Area Number |
25800094
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Tokai University (2015-2016)
Oita University (2013-2014) |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 非線形解析学 / 非線形問題 / 不動点理論 / 凸関数 / 単調作用素 / ヒルベルト空間 / バナッハ空間 / 測地的距離空間 / Bregman distance / 不動点定理 / 不動点近似 / アダマール空間 / 完備CAT(1)空間 / 近接点法 / CAT(1)空間 / 不動点 / 球面幾何 / 凸解析 / 関数解析 / 非線形作用素 / 集合値写像 |
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| Outline of Final Research Achievements |
In this research, using convex analysis for convex functions and convex sets and fixed point theory for nonlinear operators, we study the existence and approximation of solutions to several nonlinear problems. In particular, we obtain several results on the existence and approximation of fixed points of nonlinear operators in infinite dimensional linear spaces such as Hilbert spaces and Banach spaces. Applying the obtained results to minimization problems for convex functions and zero point problems for monotone operators, we obtain existence and convergence theorems for such problems. We also obtain some important results on the relation between convex minimization problems and fixed point problems in geodesic metric spaces with no linear structure.
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