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  

Common Fixed Points and the Best Approximation on Weakly Compact Sets when One of Two Mappings Is Weakly Continuous

作　　者：陈建仁[1] 

机构地区：[1]首都师范大学数学系

出　　处：《首都师范大学学报（自然科学版）》2006年第3期5-8,共4页Journal of Capital Normal University：Natural Science Edition

基　　金：国家自然科学资金(编号:10571122);北京市自然科学基金(编号:1052006)资助

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.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.

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 

分 类 号：O177.91[理学—数学] O174.41[理学—基础数学]