Nonlinear problems related to fixed point theory

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400141
• 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) ; 本田 あおい 九州工業大学, 大学院情報工学研究院, 准教授 (50271119) ; 仙葉 隆 九州工業大学, 大学院工学研究院, 教授 (30196985)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 不動点 / best proximity point / nonspreading mapping / Chatterjea mapping / ν-generalized metric / absolute norm / p-uniform convexity / q-uniform smoothness

Outline of Final Research Achievements

In these three years, we have several results in nonlinear problems related to fixed point theory. For example, we have introduced new classes of nonlinear mappings (Chatterjea mapping, Condition (CC)) and studied basic properties, existence of fixed points and convergence theorems. We have given examples of nu-generalized metric spaces that do not have the compatible topology. Also we have proved that every 3-generalized metric space has the compatible topology. We have obtained a new sufficient and necessary condition for successive approximation.

Free Research Field

不動点理論