| 弱紧集上一个映射为弱连续的映射对的公共不动点与最佳逼近 |
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| 引用本文： | 陈建仁.弱紧集上一个映射为弱连续的映射对的公共不动点与最佳逼近[J].首都师范大学学报(自然科学版),2006,27(3):5-8. |
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| 作者姓名： | 陈建仁 |
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| 作者单位： | 首都师范大学数学系,北京,100037;哈尔滨师范大学数学系,哈尔滨,150025 |
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| 基金项目： | 国家自然科学基金;北京市自然科学基金 |
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| 摘 要： | 在已有的弱紧集上的公共不动点与最佳逼近定理中,当T是I非扩张时,一般都假设仿射映射I是强(或弱)连续的.本文证明了如果用T的弱连续性代替I的强(或弱)连续性,T和I仍然有公共不动点.作为应用,文中得到了一个新的最佳逼近定理.
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| 关 键 词： | 局部凸拓扑线性空间 非扩张映射 公共不动点 最佳逼近 |
| 收稿时间： | 2005-05-06 |
| 修稿时间： | 2005年5月6日 |
Common Fixed Points and the Best Approximation on Weakly Compact Sets when One of Two Mappings Is Weakly Continuous |
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| Chen Jianren.Common Fixed Points and the Best Approximation on Weakly Compact Sets when One of Two Mappings Is Weakly Continuous[J].Journal of Capital Normal University(Natural Science Edition),2006,27(3):5-8. |
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| Authors: | Chen Jianren |
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| Institution: | Capital Normal University,Beijing 100037; Harbin Normal University, Harbin 150025 |
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| Abstract: | In the primary theorems about common fixed points and the best approximation on the weakly compact set,it was assumed that the affine mapping I was strongly(or weakly) continuous when T was I-nonexpansive.In this paper it is proved that if the strong(or weak) continuity of I is replaced by the weak continuity of T,T and I still have common fixed points.As application a new theorem on the best approximation is obtained. |
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| Keywords: | locally convex linear topological space nonexpansive mapping common fixed point the best approximation |
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