The Study of Nonlinear Functional Analysis and Nonlinear Problems Based on Fixed Point Theory and Convex Analysis

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540188
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Keio University (2013-2014); Tokyo Institute of Technology (2011-2012)
• Principal Investigator: TAKAHASHI Wataru 慶應義塾大学, 自然科学研究教育センター, 訪問教授 (40016142)
• Co-Investigator(Kenkyū-buntansha): TANIGUCHI Masaharu 岡山大学, 自然科学研究科, 教授 (30260623) ; KIMURA Yasunori 東邦大学, 理学部, 准教授 (20313447)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 非線形関数解析学 / 凸解析学 / 不動点理論 / 最適化理論 / 非線形作用素 / 均衡点問題 / 不動点アルゴリズム / バナッハ空間

Outline of Final Research Achievements

In this research, we studied nonlinear functional analysis and nonlinear problems by using fixed point theory and convex analysis. At first, we introduced the concept of attractive points of nonlinear mappings in Hilbert spaces and Banach spaces. Then we proved the existence of atrractive points and nonlinear mean convergence theorems. Furthermore, we proved weak and strong convergence theorems for semigroups of not necessarily continuous mappings in Hilbert spaces and Banach spaces. Using these theorems, we solved nonlinear problems which are important in many areas of applied mathematics.

Free Research Field

非線形関数解析学とその応用