Some new fixed point theorems of increasing operators and applications

Let E be a Banach space, P a cone in E, A:P→P an increasing operator. If there exist xO, yOεP such that xO⩽AxO, AyO⩽yO and xO⩽̸yO, then we say A satisfies two-point extension condition. We prove some fixed point theorems under two'point extension condition, and give some applications to nonlinear differential equations.