Abstract
Let E be a Banach space, P a cone in E, A:P→P an increasing operator. If there exist xO, yOeP 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.
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