一类抽象算子方程组的迭代解及其应用  

Iterative Solution for Systems of a Class of Abstract Operator Equations and Applications

作　　者：苏华[1] 刘立山[1] 吴从炘[2] 

机构地区：[1]曲阜师范大学数学科学学院,曲阜273165 [2]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《数学物理学报（A辑）》2007年第3期449-455,共7页Acta Mathematica Scientia

基　　金：国家自然科学基金(10471075;10271035);高等学校博士点专项基金(20060446001)资助

摘　　要：在Banach空间中,利用半序方法讨论了一类抽象算子方程组解的存在唯一性,推广和统一了以前的一些结果,然后应用到Banach空间非线性积分方程组,得到了方程组的唯一解,构造了收敛于方程组唯一解的迭代序列并给出了相应的误差估计。In this paper, by using partial order method, the existence and uniqueness of solutions for systems of a class of abstract operator equations in Banach spaces are studied. The results obtained in this paper improve and unify many recent results. Applications to the system of nonlinear integral equations in Banach space are given. It is proved that the unique solution exists by the iterative sequence which converges to the unique solution is constructed and the error estimate is given.

关 键 词：抽象算子方程组 唯一解 迭代序列 积分方程组 

分 类 号：O175.15[理学—数学]