Nonlinear analysis using the technique of set-valued analysis

使用集值分析技术进行非线性分析

• 批准号: 22540175
• 负责人: KIMURA Yasunori
• 金额: $ 2.83万
• 依托单位: Toho University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540175/
• 关键词: 不動点問題; 変分不等式; 均衡問題; 近似列; 測地距離空間; 非線形問題; 不動点; 凸解析

In this research, we deal with some nonlinear problems including fixed point problems and equilibrium problems, which are strongly connected to convex analysis, and consider the existence and approximation of the solutions to these problems. We focus our interest in the class of mappings which includes the resolvents of monotone operators and nonexpansive mappings and obtain some results concerning the relation between the boundedness of approximate sequences and the existence of the solution, and the convergence properties of the iterative schemes.We also consider the iterative schemes of the operators defined on complete geodesic spaces. In particular, we obtain several considerable results for the space having a curvature bounded above by a positive number. Further we obtain some important results about the convergence properties of the schemes with errors related to the computer simulation.

在本研究中，我们处理一些非线性问题，包括不动点问题和平衡问题，这是强连接到凸分析，并考虑这些问题的解的存在性和逼近。本文主要研究了一类映射，包括单调算子和非扩张映射的预解式，得到了关于逼近序列的有界性与解的存在性之间的关系以及迭代格式的收敛性的一些结果，并讨论了完备测地空间上算子的迭代格式.特别是，我们得到了几个相当可观的结果的空间有一个曲率以上有界的一个正数。进一步得到了与计算机模拟有关的带误差格式的收敛性的一些重要结果。

项目成果

Strong convergence theorems for strongly relatively nonexpansive sequences and applications

• 发表时间: 2012-02
• 期刊: arXiv: Functional Analysis
• 作者: Koji Aoyama;Y. Kimura;Fumiaki Kohsaka

A note on the hybrid steepest descent methods

• 发表时间: 2011-01
• 期刊: arXiv: Functional Analysis
• 作者: Koji Aoyama;Y. Kimura

写像列の強非拡大性

映射序列的强不可扩展性

• 发表时间: 2010
• 作者: H.Nakayama;K.Nishiyama;M.Noro;K.Ohara;T.Sei;N.Takayama;A.Takemura;木村泰紀;石田晴久;小原功任,田島慎一;K. Kajitani;青山耕治;石田晴久;田島慎一,小原功任;木下保;梶谷邦彦;Y. Kimura;小原功任,田島慎一;小原功任;K. Kajitani;Tamotu Kinoshita;Y.Kimura;梶谷邦彦;清智也,竹村彰通,小原功任,高山信毅;Hiroya Ito;小原功任,田島慎一;青山耕治
• 通讯作者: 青山耕治

堅非拡大型写像について

关于刚性不可扩展映射

• 发表时间: 2010
• 作者: Toshitaka Matsumoto;Naoki Tanaka;青山耕治
• 通讯作者: 青山耕治

The Mann iteration procedure with two nonexpansive mappings in CAT(1) spaces

CAT(1) 空间中两个非扩张映射的曼恩迭代过程

• 作者: Hubert Kalf Takashi Okaji;Osanobu Yamada;Y. Kimura and K. Nakagawa
• 通讯作者: Y. Kimura and K. Nakagawa