Z-C-X空间中的若干问题

基金项目: 江西省自然科学基金资助项目(0011022)

Some Problems in the Z-C-X Space

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

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。
- 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
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.
- Z-C-X space /
- separable real Banach space /
- random semiclosed 1-set-contractive operator /
- random solution /
- random continuous operator

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