| Project/Area Number |
16K05207
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Kyushu Institute of Technology |
|---|
Principal Investigator |
Suzuki Tomonari 九州工業大学, 大学院工学研究院, 教授 (00303173)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
加藤 幹雄 信州大学, 工学部, 非常勤講師 (50090551)
|
|---|
| Project Period (FY) |
2016-04-01 – 2024-03-31
|
| Project Status |
Completed (Fiscal Year 2023)
|
| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
|---|
| Keywords | 不動点 / contraction / ν-generalized metric / τ-distance / semimetric space / semicompleteness / 完備距離空間 / 距離完備性 / 縮小写像 / compatible な位相 / 縮小写像の条件 / Condition (B) / 解析学 |
|---|
| Outline of Final Research Achievements |
We studied fixed point theory in metric spaces. For example, we proved a new generalization of both Bogin's fixed point theorem and Ciric's fixed point theorem in complete metric spaces. In the proof, we gave a new method. Also, we introduced the concept of τ'-distance which is a very slight generalization of τ-distance and which is more natural than τ-distance. Using this concept, we proved some related theorems. In metric fixed point theory, there are several contractive conditions. We discussed these conditions by a unified method.
We studied several spaces which do not have rich structure. For example, we prove that a ν-generalized metric space has both strongly compatible topology and the strongest sequentially compatible topology. Also, we proved Caristi's fixed point theorem in (Σ,≠)-complete semimetric spaces.
|
| Academic Significance and Societal Importance of the Research Achievements |
完備距離空間における不動点理論は1960年代と1970年代に大きく発展した。その後、本質的に新しい不動点定理は証明されなかったように思える。今回得られた不動点定理は証明の手法もとても新しく、今後の発展が期待できる。τ'-distance の導入や縮小条件に関する結果は、今後の議論展開を容易にするため、新たな発展へ寄与できると思われる。
最近、 semimetric space や ν-generalized metric space といった弱い構造しか持たない空間での研究が盛んに行われている。本研究もその一部であり、得られた成果を用いて、さらに精密な研究が行われると期待できる。
|
