| 一类抽象算子方程组的迭代解及其应用 |
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| 引用本文： | 苏华,刘立山,吴从炘.一类抽象算子方程组的迭代解及其应用[J].数学物理学报(A辑),2007,27(3):449-455. |
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| 作者姓名： | 苏华 刘立山 吴从炘 |
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| 作者单位： | 曲阜师范大学数学科学学院，曲阜师范大学数学科学学院，哈尔滨工业大学数学系 曲阜 273165，曲阜 273165 哈尔滨工业大学数学系 哈尔滨 150001，哈尔滨 150001 |
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| 基金项目： | 国家自然科学基金;教育部高等学校博士学科点专项科研基金 |
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| 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.
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| 关 键 词： | 抽象算子方程组 唯一解 迭代序列 积分方程组 |
| 文章编号： | 1003-3998（2007）03-449-07 |
| 收稿时间： | 2005-09-06 |
| 修稿时间： | 2005-09-062006-10-17 |
Iterative Solution for Systems of a Class of Abstract Operator Equations and Applications |
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| Su Hua,Liu Lishan,Wu Congxin.Iterative Solution for Systems of a Class of Abstract Operator Equations and Applications[J].Acta Mathematica Scientia,2007,27(3):449-455. |
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| Authors: | Su Hua Liu Lishan Wu Congxin |
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| Institution: | 1.School of Mathematical Sciences, Qufu Normal University, Qufu 273165; 2.Department of Mathematics, Harbin Institute of Technology, Harbin 150001 |
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| Abstract: | 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. |
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| Keywords: | Systems of abstract operator equations Unique solution Iterative sequences Systems of integral |
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