| 混合单调算子的两点拉伸型不动点定理 |
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| 引用本文： | 刘进生,李福义.混合单调算子的两点拉伸型不动点定理[J].数学学报,2003,46(6):1117-112. |
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| 作者姓名： | 刘进生 李福义 |
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| 作者单位： | 1. 太原理工大学数学系,太原,030024
2. 山西大学数学系,太原,030006 |
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| 基金项目： | 山西省青年科技基金资助项目(20021001) |
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| 摘 要： | 本文首次提出了混合单调算子不动点的两点拉伸型条件.同时,利用锥映象的不动点指数理论建立了一类特殊的两点拉伸型混合单调算子的不动点存在性定理,并将所得结论应用于带有超线性项的积分方程与微分方程上,得到了新的结论.因而在本质上推进了混合单调算子不动点问题的研究.
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| 关 键 词： | 混合单调算子 两点拉伸型条件 锥 |
| 文章编号： | 0583-1431(2003)06-01117-06 |
| 修稿时间： | 2001年10月15 |
Two-Point Expansion Fixed Point Theorems of Mixed Monotone Operators |
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| Jin Sheng LIU.Two-Point Expansion Fixed Point Theorems of Mixed Monotone Operators[J].Acta Mathematica Sinica,2003,46(6):1117-112. |
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| Authors: | Jin Sheng LIU |
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| Institution: | Jin Sheng LIU
(Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P. R. China)
(E-mail: L_J_S@163.com)
Fu Yi LI
(Department of Mathematics, Shanxi University, Taiyuan 030006, P. R. China) (E-mail: fyli@sxu.edu.cn) |
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| Abstract: | In this paper, the two-point expansion condition of fixed point for the mixed monotone operator is first given, and some existence theorems for fixed point for a special class of two-point expansion mixed monotone operators are established by using the fixed point index theory for operators from a cone to itself. The results obtained here are applied to Hammerstein integral equations and two-point boundary value problems for a fourth order differential equation and therefore some new conclusions are obtained. |
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| Keywords: | Mixed monotone operator Two-point expansion condition Cone |
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