| Z-C-X空间中的若干问题 |
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| 引用本文： | 朱传喜. Z-C-X空间中的若干问题[J]. 应用数学和力学, 2002, 23(8): 837-842 |
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| 作者姓名： | 朱传喜 |
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| 作者单位： | 1.西安交通大学, 应用数学研究中心, 信息与系统科学研究所, 西安, 710049; |
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| 基金项目： | 江西省自然科学基金资助项目 (0 0 110 2 2 ) |
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| 摘 要： | 提出了Z-C-X空间以及优锥的新概念,在Z-C-X空间中研究了随机半闭1-集压缩算子的若干问题。首先,证明了一个重要的不等式。其次,利用随机拓扑度理论中的随机不动点指数证明了几个新的结论。在仿平行四边形律之条件下得到了一类随机算子方程的随机解,在偏序的Z-C-X空间中推广了着名的Altman定理。因此,得到了若干新的结果。
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| 关 键 词： | Z-C-X空间 可分的实Banach空间 随机半闭1-集压缩算子 随机解 随机连续算子 |
| 文章编号： | 1000-0887(2002)08-0837-06 |
| 收稿时间： | 2001-03-30 |
| 修稿时间： | 2001-03-30 |
Some Problems in the Z-C-X Space |
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| ZHU Chuan_xi . Some Problems in the Z-C-X Space[J]. Applied Mathematics and Mechanics, 2002, 23(8): 837-842 |
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| Authors: | ZHU Chuan_xi |
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| Affiliation: | 1.Research Center for Applied Mathematics and Institute of Information and System Science, Xi'an Jiaotong University, Xi'an 710049, P.R.China;2.Institute of Mathematics, Nanchang University, Nanchang 330029, P.R.China |
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| Abstract: | The new concepts of the Z-C-X space and excellent cone are introduced.Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space.At first,an important inequality is proved.Secondly,several new conclusions are proved by means of random fixed point index in the theory of random topological degree.A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained,famous Altman.s theorem is generalized in partially ordered Z-C-X space.Therefore,some new results are obtained. |
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