Hilbert空间中非扩张映像族公共不动点的存在性

The existence of common fixed points for a family of nonexpansive mappings in Hilbert spaces

摘要: 在Hilbert空间中,首先利用距离投影算子技巧证明了由Aoyama,Kohsaka和Takahashi构造的关于非扩张映像族的收缩投影方法所生成的序列是有意义的;其次获得了非扩张映像族有公共不动点的几个充分必要条件.

Abstract: It is proved that the sequence generated by Aoyama,Kohsaka and Takahashi's shrinking projection method for a family of nonexpansive mappings is well defined by using metric projection operator technique,and then many necessary and sufficient conditions are obtained for the family of nonexpansive mappings having a common fixed point in a Hilbert space.