混合单调映象的压缩映象原理及其应用(英文)

Contraction mapping principle of mixed monotone mapping and application

利用单调迭代技巧 ,建立半序度量空间中混合单调映象的压缩映象原理 ,然后运用它研究半序Banach空间中某些不具有连续性和紧性条件的非线性二元算子的不动点的存在唯一性及迭代收敛性 ,最后给出所得结果对Hammerstein型非线性积分方程的应用。

This paper establishes the contraction mapping principle for mixed monotone mapping in partial ordering metric space by means of monotone iterative techniques, and then applies it to study the existence, uniqueness and iterative approximation of fixed point for some nonlinear binary operators which do not posses any continuity and compactness conditions in partial ordering Banach space. Finally, the application of our results to Hammerstein type nonlinear integral equations is worked out.