2016 Fiscal Year Final Research Report
A study on nonlinear problems using convex analysis and fixed point theory
| Project/Area Number |
25800094
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Foundations of mathematics/Applied mathematics
|
|---|
| Research Institution | Tokai University (2015-2016)
Oita University (2013-2014) |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2013-04-01 – 2017-03-31
|
| 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 |
|---|
| 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.
|
| Free Research Field |
非線形解析学とその応用
|
