2010 Fiscal Year Final Research Report
The Study of Nonlinear Functional Analysis and Convex Analysis and its Applications Based on Optimization Theory and Fixed Point Theory
| Project/Area Number |
19540167
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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 | Tokyo Institute of Technology |
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Principal Investigator |
TAKAHASHI Wataru Tokyo Institute of Technology, 経済学部, 教授 (40016142)
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| Co-Investigator(Kenkyū-buntansha) |
TANIGUCHI Masaharu 東京工業大学, 情報理工学研究科, 准教授 (30260623)
KIMURA Yasunori 東京工業大学, 情報理工学研究科, 助教 (20313447)
KOMIYA Hidetoshi 慶應義塾大学, 商学部, 教授 (90153676)
KIDO Kazuo 慶應義塾大学, 商学部, 教授 (50286621)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 関数解析学 / 凸解析学 / 不動点理論 / 最適化理論 / 非線形作用素 |
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| Research Abstract |
In this study, we obtain many new and important theorems for nonlinear problems in nonlinear functional analysis and convex analysis by using optimization theory and fixed point theory. For example, we solved an open problem in geometry of Banach spaces which has been posed by Ray in 1980 by proving that every nonspreading mapping of a nonempty closed convex subset of a reflexive, strictly convex and smooth Banach space into itself has a fixed point if and only if the set is bounded.
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