新的二元算子方程组解的存在唯一性定理
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摘要
利用锥理论和单调迭代方法,在更一般的条件下得到了一类新的不具有连续性和紧性条件的非单调二元算子方程组解的存在唯一性,并给出迭代误差估计,所得结果改进和推广了最近的一些已知结果.
In this paper,by using the cone theory and the monotonous iteration method,we obtain the existence and uniqueness of solutions of a system of nonmonotone binary equations without continuity and compactness conditions under more general conditions.The error estimates are also given.The results given here improve and generalize some known results.
In this paper,by using the cone theory and the monotonous iteration method,we obtain the existence and uniqueness of solutions of a system of nonmonotone binary equations without continuity and compactness conditions under more general conditions.The error estimates are also given.The results given here improve and generalize some known results.
引文
[1]Guo D J,Lakthmikantham V.Coupled fixed points of nonhnear operators with apphcations.Nonlinear Anal.,1987,11(5):623-632.
[2]Yan X L.Existence and uniqueness theorems of solution for symmetric contraction operator equations and their apphcations.Chinese Science Bulletin,1991,36(10):800-805.
[3]Sun Y.A fixed point theorem for mixed monotone operators with application.J.Math.Anal.AppL,1991,156:240-252.
[4]Chen YZ.Existence theorems of coupled fixed points.J.Math.Anal.AppL,1991,154:142-150.
[5]张克梅.非线性非单调算子方程的解.数学物理学报,1998,18(2):164-168.
[6]吴焱生,李国桢.混合单调算子的不动点存在唯一性定理及其应用.数学学报,2003,46(1):161-16.
[7]孙经先,刘立山.非线性算子方程的迭代求解及应用.数学物理学报,1993,3:141-145.
[8]刘立山.Banach空间非线性混合单调Hammerstein型积分方程的迭代解.系统科学与数学,1996,16(4):338-343.
[9]张晓燕,刘立山.非线性算子方程迭代解的存在性定理及其应用.数学物理学报,2001,21A(3):398-404.
[10]张培国,刘立山.序Banach空间非混合单调二元算子不动点的存在唯一性及应用.数学学报,2010,53(1):55-60.
[11]刘炳妹,刘立山.二阶方程组解的存在唯一性.工程数学学报,2007,24(4):757-760.
[12]栾世霞,孙钦福.混合单调算子方程组解的存在唯一性定理.工程数学学报,2009,26(2):373-376.
[13]李波,原新生.一类二元算子方程组的公共不动点.安徽大学学报,2011,35(1):32-36.
[14]郭大钧.非线性分析中的半序方法.济南:山东科学技术出版社,2000.
[2]Yan X L.Existence and uniqueness theorems of solution for symmetric contraction operator equations and their apphcations.Chinese Science Bulletin,1991,36(10):800-805.
[3]Sun Y.A fixed point theorem for mixed monotone operators with application.J.Math.Anal.AppL,1991,156:240-252.
[4]Chen YZ.Existence theorems of coupled fixed points.J.Math.Anal.AppL,1991,154:142-150.
[5]张克梅.非线性非单调算子方程的解.数学物理学报,1998,18(2):164-168.
[6]吴焱生,李国桢.混合单调算子的不动点存在唯一性定理及其应用.数学学报,2003,46(1):161-16.
[7]孙经先,刘立山.非线性算子方程的迭代求解及应用.数学物理学报,1993,3:141-145.
[8]刘立山.Banach空间非线性混合单调Hammerstein型积分方程的迭代解.系统科学与数学,1996,16(4):338-343.
[9]张晓燕,刘立山.非线性算子方程迭代解的存在性定理及其应用.数学物理学报,2001,21A(3):398-404.
[10]张培国,刘立山.序Banach空间非混合单调二元算子不动点的存在唯一性及应用.数学学报,2010,53(1):55-60.
[11]刘炳妹,刘立山.二阶方程组解的存在唯一性.工程数学学报,2007,24(4):757-760.
[12]栾世霞,孙钦福.混合单调算子方程组解的存在唯一性定理.工程数学学报,2009,26(2):373-376.
[13]李波,原新生.一类二元算子方程组的公共不动点.安徽大学学报,2011,35(1):32-36.
[14]郭大钧.非线性分析中的半序方法.济南:山东科学技术出版社,2000.