一类非单调二元算子方程及方程组的迭代解法

数学季刊 ›› 2004, Vol. 19 ›› Issue (1): 69-74.

一类非单调二元算子方程及方程组的迭代解法

1. Department of Mathematics, Shangqiu Teacher's College, Shangqiu 476000, China; 2. Department of Print Engineering, the Advanced College of Shanghai Publishing Print, Shanghai 200093, China

收稿日期:2002-06-10 出版日期:2004-03-30 发布日期:2024-03-27
作者简介:ZHANG Fei-ran(1972-),male,native of Xiayi,Henan,a lecturer of Shangqiu Teacher's College, engages in nonlinear functional with applications;ZHOU Xiao-zhong(1963-),male,native of Wuyang,Henan, an associate professor of the Advanced College of Shanghai Publishing Print,engages in algebra.
基金资助:
Supported by the Scientific Research Foundation of Henan Provincial Education Com mittee(1999110018)；

Iterative Solutions for a Non-monotone Binary Operator Equations and Operator System of Equations

1. Department of Mathematics, Shangqiu Teacher's College, Shangqiu 476000, China; 2. Department of Print Engineering, the Advanced College of Shanghai Publishing Print, Shanghai 200093, China

Received:2002-06-10 Online:2004-03-30 Published:2024-03-27
About author:ZHANG Fei-ran(1972-),male,native of Xiayi,Henan,a lecturer of Shangqiu Teacher's College, engages in nonlinear functional with applications;ZHOU Xiao-zhong(1963-),male,native of Wuyang,Henan, an associate professor of the Advanced College of Shanghai Publishing Print,engages in algebra.
Supported by:
Supported by the Scientific Research Foundation of Henan Provincial Education Com mittee(1999110018)；

摘要/Abstract

摘要： By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A₁+A₂, B=B₁+B₂, A₁ and B₁ are mixed monotone, A₂ and B₂ are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.

关键词: cone , and , partial ordering, operator equations, anti-mixed monotone

Abstract: By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A₁+A₂, B=B₁+B₂, A₁ and B₁ are mixed monotone, A₂ and B₂ are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.

Key words: cone , and , partial ordering, operator equations, anti-mixed monotone

中图分类号:

O177.91

张斐然, 周晓中. 一类非单调二元算子方程及方程组的迭代解法[J]. 数学季刊, 2004, 19(1): 69-74.

ZHANG Fei-ran, ZHOU Xiao-zhong . Iterative Solutions for a Non-monotone Binary Operator Equations and Operator System of Equations[J]. Chinese Quarterly Journal of Mathematics, 2004, 19(1): 69-74.

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