反向混合单调算子的不动点存在唯一性定理及其应用

On the fixed point existence and uniqueness theorems of anti-mixed monotone operators and their applications

讨论了一类反向混合单调算子方程组的存在唯一性及非对称迭代逼近问题,得到了若干不具有连续性和紧性条件的有关反向混合单调算子、增算子、减算子的新不动点定理.最后,将所得结果应用于R N上的Hammerstein积分方程之中.

This paper firstly discusses the existence, uniqueness and oon-systemetric iterative approximation of solution for a class of systems of anti-mixed monotone operator equations, and obtains some new fixed point theorems of anti-mixed monotone operators, increasing operators and decreasing operators which have no continuous and compact conditions. Finally, the new results presented in this paper are applied to Hammerstein integral equations on R^N.