迭代序列逼近非线性映像不动点集的一个几何结构

被引:2
作者
苏永福 [1 ]
周海云 [2 ]
机构
[1] 天津工业大学理学院数学系
[2] 中国科技大学理学院数学系
关键词
Hilbert空间; 收敛序列; 几何结果;
D O I
暂无
中图分类号
O177.91 [非线性泛函分析];
学科分类号
070104 ;
摘要
设E是Hilbert空间,T:D(T)→R(T)是E中具非空不动点集F(T)的非线性映像,许多非线性映像的多种形式的迭代序列{X_n}可逼近映像T的不动点p0∈F(T),并且逼近过程{X_n}与不动点集F(T)有密切的几何关系,其中一种几何关系可描述为钝角原理,其准确表述为lim sup_n→+∞〈p—p0,■〉■0,■p∈F(T).或令θ_n(p)=arccos〈■〉,■p∈F(T).钝角原理可表述为liminf_n→+∞θ_n(p)■π/2.在相应条件下,具有这种几何关系的非线性映像包括非扩张映像、渐近非扩张映像、Lipschitz映像、增生映像、伪压缩映像、渐近伪压缩映像、严格伪压缩映像、强伪压缩映像等大量非线性映像.钝角原理一方面可揭示非线性映像不动点逼近过程的几何结构,也是迭代逼近非线性映像不动点的必要条件.
引用
收藏
页码:1321 / 1326
页数:6
相关论文
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