Mixed monotone operators of the new fixed point theorems and its application.

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 mathematical 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 related 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. [ABSTRACT FROM AUTHOR]