在锥度量空间中，由一类混合单调算子的不动点定理扩展到两类混合单调算子的公共不动点定理。同时证明了增算子的不动点定理。

In this paper the fixed point theorems for a class of mixed monotone operators are extended to two classes of mixed monotone operators in cone metric space. Furthermore, it proves the fixed point theorem of increasing operator.

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 .

在半序空间X×X中证明了具A=CB形式的混合单调算子的耦合不动点定理和最小最大耦合不动点定理.最后将该定理应用于讨论含有不连续项的混合单调Volterra型积分方程耦合拟解的存在性.

Assuming X × X is partly ordered space,some coupled fixed point theorems and coupled minimal-maximal fixed points of mixed monotone operators which are expressed as the form A=CB are obtained. As an application, the existence of coupled quasi-solutions for mixed monotone Volterra integral equations with discontinuous terms is discussed.