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迭代序列逼近非线性映像不动点集的一个几何结构 被引量:1

A Geometric Result for Approximating Fixed Points of Nonlinear Mappings by Iteration Sequence
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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{xn}可逼近映像T的不动点P0∈F(T),并且逼近过程{xn}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 supn→+∞〈p—P0,xn-po/||xn-p0||〉≤0,任意p∈F(T).或令θn(p)=arccos〈p-p0/p-p0,xn-po/||xn-p0||〉,任意p∈F(T).钝角原理可表述为lim infn→+∞θn(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. LetE be a Hilbert space, T : D(T) → R(T) be a nonlinear mapping with nonempty set of fixed points. For a lot of nonlinear mappings, the fixed points can be approximating by iteration sequence{xn}. In the approximating process, a geometric result can be expressed as limsupn→+∞〈p-P0xn-po/||xn-p0||〉≤0,arbitary p E F(T). Equvalently, putting θn(p)=arccos〈p-p0/p-p0,xn-po/||xn-p0||〉, arbitaryp ∈ F(T). then limsupn→+∞θn(p)≥π/2. This geometric result is said to be an obtuse angle principle. In the relevant condition, the obtuse angle principle holds for nonexpansive mappings, asymptotically nonex- pansive mappings, Lipschitz mappings, accretive mappings, pseudocontractive mappings, asymptotically pseudocontractive mappings, strictly pseudocontractive mappings, strongly pseudocontractive mapping, etc.
作者 苏永福 周海云 Yong Fu SU,Hai Yun ZHOU(Department of Mathematics, School of Science, Tianjin Polytechnic University, Tianjin 300160, P. R. China Department of Mathematics, School of Science, University of Science and Technology of China, Hefei 230036, P. R. China Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, P. R. China)
出处 《数学学报》 SCIE CSCD 北大核心 2006年第6期1321-1326,共6页 Acta Mathematica Sinica
基金 国家自然科学基金资助项目(10741033) 天津市学科建设基金资助项目(100580204)
关键词 HILBERT空间 收敛序列 几何结果 Hilbert space convergent sequence geometric results
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参考文献37

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