序Banach空间中算子方程的迭代求解及其应用

Iterative Solution of Operator Equations in Ordered Banach Spaces with Applications

利用半序理论和混合单调算子技巧 ,研究序 Banach空间中非线性算子方程解的存在唯一性 ,并给出了迭代序列收敛于解的误差估计 .作为应用 ,讨论了序 Banach空间中一类非线性积分方程的可解性 ,改进和推广了某些已知结果 .

With the partial order theory and monotone iterative technique, the ex istence and uniqueness of the solution for the nonlinear operator equations are studied, and the error estimations for the convergent iterative sequence are als o given. As the applications of the main results, the solvability for a class of nonlinear integral equations in ordered Banach spaces are discussed. Some known results on iterative solution of operator equations are improved and generalize d.