| 混合单调算子的不动点存在唯一性定理及其应用 |
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| 引用本文： | 吴焱生,李国祯.混合单调算子的不动点存在唯一性定理及其应用[J].数学学报,2003,46(1):161-166. |
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| 作者姓名： | 吴焱生 李国祯 |
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| 作者单位： | 江西师范大学数学系,南昌,330027 |
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| 基金项目： | 江西省自然科学基金资助项目(991 1003) |
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| 摘 要： | 本文首先讨论了一类混合单调算子方程组解的存在唯一性及非对称迭代逼近问题,得到了若干不具有连续性和紧性条件的有关混合单调算子、增算子和减算子的新不动点定理.其次研究了具有a-凹和-a-凸的不具有连续性和紧性条件的混合单调算子的不动点,并得到了一个新结果.最后,我们将所得结果应用于RN上的Hammerstein积分方程之中(参见文1-12]).
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| 关 键 词： | 正规锥 混合单调算子 α-凹算子 -α-凸算子 不动点 |
| 文章编号： | 0583-1431(2003)01-0161-06 |
| 修稿时间： | 2000年6月12日 |
On the Fixed Point Existence and Uniqueness Theorems of Mixed Monotone Operators and Their Applications |
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| Yan Sheng WU Quo Zhen LI.On the Fixed Point Existence and Uniqueness Theorems of Mixed Monotone Operators and Their Applications[J].Acta Mathematica Sinica,2003,46(1):161-166. |
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| Authors: | Yan Sheng WU Quo Zhen LI |
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| Institution: | Yan Sheng WU Quo Zhen LI(Department of Mathematics, Jiangxi Normal University, Nanchang 330027, P. P. China) (E-mail: lgnbox@public.nc.jx.cn) |
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| Abstract: | In this paper, we firstly discuss the existence, uniqueness and non-symmetric iterative approximation of solution for a class of systems of mixed monotone operator equations, and obtain some new fixed point theorems of mixed monotone operators, increasing operators and decreasing operators which have no continuous and compact conditions. Secondly, we study the fixed point of mixed monotone operators which have a-concave and -a-convex conditions while the operators also have no continuous and compact conditions, and get a new result. Finally, we apply the new results presented in this paper to Hammerstein integral equations on RN (see 1-12]). |
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| Keywords: | Normal cone Mixed monotone operator a-concave operator -a-convex operator Fixed point |
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