CAJ | 학술논문

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。
이용단조질대법、수학귀납법이급서차적성질대반서Banach공간중적반향혼합단조산자급혼합단조산자대적불동점존재성화유일성진행연구。득도료타문재모충서차관계하적신적불동점정리，대상관결론진행료추엄，병장혼합단조산자대불동점정리응용우구해일계상미분방정조적초치문제중。
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 .