摘要
利用单调迭代法、数学归纳法以及序差的性质对半序Banach空间中的反向混合单调算子及混合单调算子对的不动点存在性和唯一性进行研究.得到了它们在某种序差关系下的新的不动点定理,对相关结论进行了推广,并将混合单调算子对不动点定理应用于求解一阶常微分方程组的初值问题中.
In order to explore the existence and uniqueness of reverse mixed monotone operators and the mixed monotone operatorin partially ordered Banach space ,the monotone iterative method and mathe-matical induction as well as the properties of the ordering difference are used .Then the new fixed point theorems of them under some ordering difference relationship is obtained .The results generalize the re-lated conclusion .Finally the fixed point theorems of the mixed monotone operators are applied to initial value problem of the first order ordinary differential equation group .
出处
《纺织高校基础科学学报》
CAS
2014年第3期328-331,共4页
Basic Sciences Journal of Textile Universities
基金
陕西省自然科学基金资助项目(2012JM1017)
关键词
混合单调算子
正规锥
不动点
序差
归纳法
mixed monotone operators
normal cone
fixed point
ordering difference
conjecture
