| 不具有关于锥的例外簇的映射 |
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| 引用本文： | 黄龙光,刘三阳.不具有关于锥的例外簇的映射[J].数学研究,2002,35(1):44-48. |
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| 作者姓名： | 黄龙光 刘三阳 |
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| 作者单位： | 1. 西安电子科技大学应用数学系,陕西,西安,710071,韩山师范学院数学系,广东,潮州,521041
2. 西安电子科技大学应用数学系,陕西,西安,710071 |
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| 基金项目： | 国家自然科学基金资助项目 (6 9972 0 36 )，陕西省自然科学研究项目 (2 0 0 0SL0 3) |
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| 摘 要： | 给出Hilbert空间到其自身不具有关于锥的例外族的映射条件，利用Hilbert空间可表为闭凸锥与负对偶锥的特点研究映射关于锥的例外簇的特性，证明了可通过映射在某紧凸子集上的性态判断其例外簇的存在与否，并讨论单调和沿射线单调映射的不具例外簇问题。
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| 关 键 词： | 闭凸尖锥 例外簇 单调映射 沿射线单调 伪单调 Hilbert空间 变分不等式 |
| 修稿时间： | 2001年5月8日 |
The Mappings without Exceptional Family with Respect to a Cone |
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| Huang Longguang , Liu Sanyang.The Mappings without Exceptional Family with Respect to a Cone[J].Journal of Mathematical Study,2002,35(1):44-48. |
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| Authors: | Huang Longguang Liu Sanyang |
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| Institution: | Huang Longguang 1,2 Liu Sanyang 1 |
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| Abstract: | The conditions that mappings from a Hilbert space to itself have no exceptional family with respect to a cone are presented. The conception is based on the feature of Hilbert space that can be expressed as the sum of a closed convex cone and its negative dual cone. The results obtained show that characteristics of mappings in a compact subset of cone determine whether or not the exceptional family exists. Meanwhile, problems of no exceptional family on the several kinds of monotone mappings are studied. |
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| Keywords: | closed convex pointed cone exceptional family monotone mapping pseudomonotone monotone on ray |
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