Banach空间中渐近非扩张映象具误差的强收敛定理  

Strong Convergence Theorem for Asymptotically Nonexpansive Mappings with Errors in Banach Spaces

作　　者：赵良才[1] 张石生[1] 

机构地区：[1]宜宾学院数学系,宜宾644000

出　　处：《数学学报（中文版）》2008年第1期99-108,共10页Acta Mathematica Sinica：Chinese Series

摘　　要：设E是一实的Banach空间,其范数是一致Gteaux可微的;D是E的一非空闭凸子集,设T:D→D是具有序列{k_n}[1,∞),lim_(n→∞) k_n=1的渐近非扩张映象.本文证明了,在一定条件下,由(1.3)和(1.5)式定义的具误差的迭代序列{x_n}强收敛于T的不动点.本文结果也推广和改进了最近一些人的最新结果.Let E be a real Banach space with a uniformly Gateaux differentiable norm, D be a nonempty closed convex subset of E and T ： D → D be an asymptotically nonexpansive mapping with a squence {kn} [1, ∞）, kn → 1. It is shown that under some suitable conditions, the sequence with errors {xn} defined by （1.3） and （1.5） converges strongly to some fixed points of T. The results presented in this paper also extend and improve some recent results.

关 键 词：不动点 渐近非扩张映象 具误差的迭代序列 

分 类 号：O177.91[理学—数学]