Banach空间中非扩张映像的强收敛性

Strong Convergence for Nonexpansive Mappings in Banach Spaces

在实光滑和一致凸Banach空间中通过引入广义度量投影,证明了一个关于非扩张映像的修正Mann迭代序列的强收敛性定理。目的是利用广义度量投影来修改Nakajo与Takahashi的迭代方案,并将Nakajo与Takahashi文中所对应的主要结果由Hilbert空间推广到实光滑和一致凸Banach空间。

In this paper, it is shown that in a real smooth and uniformly convex Banaeh space, a strong convergence theorem of modified Mann iterations for nonexpansive mappings is proved by using generalized metric projections. The purpose of this paper is to modify the iterative scheme of Nakajo and Takahashi by using generalized metric pro- jections, and to extend the corresponding main result of Nakajo and Takahashi from Hilbert spaces to real smooth and uniformly convex Banach spaces.