2013 Fiscal Year Final Research Report
Nonlinear Analysis and Convex Analysis by fixed point theory and its Application to Equilibrium problems and Nonlinear Optimization
| Project/Area Number |
22540120
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | University of Yamanashi |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
HIRANO Norimichi 横浜国立大学, 環境情報研究院, 教授 (80134815)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 不動点 / 凸解析 / 最適化問題 / 均衡問題 / 非拡大写像 / 非拡大半群 / イタレーション / 収束 |
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| Research Abstract |
In this study, we obtain many new and important theorems for nonlinear problems in nonlinear analysis and convex analysis by using fixed point theory. For example, we studied common attractive points and proved nonlinear ergodic theorems for nonexpansive semigroups without convexity. And, we proved strong convergence to common attractive points of nonexpansive semigroups. Further, we proved strong convergence theorems for uniformly asymptotically regular nonexpansive semigroup in Banach spaces by Halpern type and Browder type iterations.
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