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，我们处理一些与凸分析密切相关的非线性问题，包括不动点问题和平衡问题，并考虑这些问题解的存在性和近似性。我们将兴趣集中在映射类上，其中包括单调算子和非扩张映射的求解，并获得了关于近似序列的有界性与解的存在性之间的关系以及迭代方案的收敛性质的一些结果。考虑在完整测地线空间上定义的算子的迭代方案。特别是，对于曲率以正数为界的空间，我们获得了几个重要的结果。此外，我们还获得了一些关于具有与计算机模拟相关的误差的方案的收敛特性的重要结果。

项目成果

Convergence of a sequence of sets in a Hadamard space and the shrinking projection method for a real Hilbert ball

Hadamard空间中集合序列的收敛性和真实希尔伯特球的收缩投影方法

• DOI: 10.1155/2010/582475
• 发表时间: 2010
• 期刊: Abstract and Applied Analysis
• 作者: N. Fukuda;T. Kinoshita;T. Kubo;Y. Kimura
• 通讯作者: Y. Kimura

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

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

Shrinking projection method for quasinonexpansive mappings on the unit shpere of a Hilbert space

希尔伯特空间单位球面上拟非扩张映射的收缩投影方法

• 发表时间: 2011
• 作者: Y.Kimura;K.Sato
• 通讯作者: K.Sato

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