关于随机定点1-集压缩算子

On Random Constant Point 1-Set-Contractive Operator

在一般可分的实Banach空间中,引入了一类新的随机算子,提出了若干随机定点1-集压缩算子的新概念,研究了这些随机定点1-集压缩算子的随机不动点.在一般框架下,对该类算子建立了随机不动点定理,从而推广了非线性泛函分析中著名的Rothe定理.利用随机拓扑度,证明了Z1型至Z4型随机定点1-集压缩算子有随机不动点的结论.

In general separable real Banach space,a class of new random operators are introduced.Some new concepts of random constant point 1-set-contractive operator were proposed. In addition, these random fixed points of random constant point 1-set-contractive operator were investigated.In ordinary frame,random fixed theorems were established for the kind of operators. Thus famous Rothe′s theorem in nonlinear functional analysis can be generalized.By means of random topological degree, the conclusion is confirmed that each of random constant point 1-set-contractive operator from Z_1 to Z_4 type has random fixed point.