| 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 |
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| 引用本文： | 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[J].数学学报,2010,53(1):55-60. |
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| 作者姓名： | 张培国 刘立山 |
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| 作者单位： | 曲阜师范大学数学科学学院;菏泽学院初等教育系; |
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| 基金项目： | 国家自然科学基金资助项目(10771117); 高等学校博士点科研基金(20060446001); 山东省自然科学基金(Y2007A23); 曲阜师范大学博士科研启动经费(Bsqd2007040) |
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| 摘 要： | 利用锥理论和Banach压缩映象原理在更一般的条件下建立了序Banach空间中一类非混合单调二元算子不动点的存在唯一性定理,并应用到Banach空间中二阶非线性Volterra型微分-积分方程初值问题,改进并推广了已有的一些结果.
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| 关 键 词： | 锥理论 非混合单调二元算子 算子不动点 |
| 收稿时间： | 2008-05-29 |
| 修稿时间： | 2009-03-17 |
Existence and Uniqueness of Fixed Points for Mixed Non-Monotone Binary Operators in Ordered Banach Spaces and Its Applications |
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| Pei Guo ZHANG School of Mathematical Sciences,Qufu Normal University,Qufu ,P.R.China.Existence and Uniqueness of Fixed Points for Mixed Non-Monotone Binary Operators in Ordered Banach Spaces and Its Applications[J].Acta Mathematica Sinica,2010,53(1):55-60. |
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| Authors: | Pei Guo ZHANG School of Mathematical Sciences Qufu Normal University Qufu PRChina |
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| Institution: | 1. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, P. R. China;
2. Department of Elementary Education, Heze University, Heze 274000, P. R. China |
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| Abstract: | By using the cone theory and the Banach contraction mapping principle, the existence and uniqueness theorem of fixed points for mixed non-monotone binary operators in ordered Banach spaces are investigated under more general condition. As an application,an existence and uniqueness theorem of solutions for initial value problems of second order nonlinear integro-differential equations of Volterra type in Banach spaces is given.The results presented here improve and generalize some known results. |
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| Keywords: | cone theory mixed non-monotone binary operators fixed points of operator |
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