Banach空间中渐近非扩张映象的收敛性

The Convergence for Asymptotically Nonexpansive Mappings in Banach Spaces

在Banach空间中引入和研究渐近非扩张映象的某些类型迭代序列的收敛性,利用Banach压缩映象原理,采用误差迭代和不等式技巧,获得了Banach空间中渐近非扩张映象的相应序列强收敛的充分必要条件,其结果改进和推广了最新的一些结果.

In this paper, we first introduce some iterative processes for asymptotically nonexpansive mappings in Banach spaces and then discuss the strong convergence for the iterative processes. By using Banach compression image principle and applying iterative scheme with errors and inequality technique, the necessary and sufficient conditions for the strong convergence of the iterative sequence of asymptotically nonexpansive mappings in Banach spaces are obtained. The results presented in this paper extend and improve some recent results in literature.