Some new fixed point theorems of increasing operators and applications

Abstract

Let E be a Banach space, P a cone in E, A:P→P an increasing operator. If there exist x_O, y_OεP such that x_O⩽Ax_O, Ay_O⩽y_O and x_O⩽̸y_O, 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.

Keywords:

• Fixed point
• cone
• increasing operator

AMS(MOS)::

• 47H10