The study of nonlinear functional analysis and nonlinear problem based on fixed point theory and convex analysis, and its applications
| Project/Area Number |
26400196
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Foundations of mathematics/Applied mathematics
|
|---|
| Research Institution | University of Yamanashi |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
SHIOJI Naoki 横浜国立大学, 大学院・工学研究院, 教授 (50215943)
|
|---|
| Project Period (FY) |
2014-04-01 – 2018-03-31
|
| Project Status |
Completed (Fiscal Year 2017)
|
| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
|---|
| Keywords | 不動点理論 / 非線形関数解析学 / 不動点近似 / 凸解析学 / 関数解析学 / 点列近似法 / 非線形エルゴード理論 / 不動点 / attractive point / acute point / 最適化問題 / イタレーション / 収束 / エルゴード定理 / 非拡大写像 / 非拡大半群 / 凸解析 |
|---|
| Outline of Final Research Achievements |
In this research, we study nonlinear functional analysis and nonlinear problems by using fixed point theory and convex analysis. We introduced the concepts of common attractive points of families of nonlinear mappings and acute points of nonlinear mappings. We proved the basic theorems concerned with the concepts. Further, we prove nonlinear ergodic theorems for semigroups of nonlinear mappings without convexity by using the concepts of common atractive points of the semigroups. We also proved weak and strong convergence theorems for nonlinear mappings by using the concepts of acute points. Using these theorems, we studied important nonlinear problems.
|
Report
(5 results)
Research Products
(59 results)
