The study of nonlinear functional analysis and nonlinear problem based on fixed point theory and convex analysis, and its applications

2017 Fiscal Year Final Research Report

• 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: ATSUSHIBA Sachiko 山梨大学, 大学院総合研究部, 准教授 (20327761)
• 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
• 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

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.

Free Research Field

非線形関数解析学