Lipschitz条件下混合单调算子对的不动点及其应用

Fixed point of mixed monotone operator and its application under the conditions of Lipschitz

在Lipschitz条件下,应用归纳法,半序方法对混合单调算子对的不动点的存在性及唯一性进行了证明,得出了混合单调算子对的不动点的存在性及唯一性,求出了迭代序列及误差估计,并将该结论应用于带奇性的一阶非线性常微分方程组的初值问题.

In the Lipschitz conditions, we prove the existence and the unique of the mixed monotone operator with induction and half sequence method. It is concluded that the mixed monotone operator of the fixed point to the existence and uniqueness, and find the iterative sequences and the error estimation. Finally we give the application in differential equation group.