Banach空间中Reich-Takahashi迭代法的强收敛定理  

Strong Convergence Theorems of the Modified Reich-Takahashi Iteration Method in Banach Spaces

作　　者：曾六川[1] 

机构地区：[1]上海师范大学数学系,上海200234

出　　处：《数学学报（中文版）》2005年第3期417-426,共10页Acta Mathematica Sinica：Chinese Series

基　　金：教育部高校优秀青年教师教学和科研奖励基金上海市教委高校科技发展基金科委重大项目基金(部分)资助上海市曙光计划基金资助项目

摘　　要：设E是具有一致正规结构的实Banach空间,其范数是一致Gateaux可微的;设D是E的非空有界闭凸子集,T:D→D是渐近非扩张映象.本文证明了,在一些适当的条件下,由修正的Reich-Takahashi迭代法(1.2)式所定义的序列{xn}强收敛到渐近非扩张映象的不动点,其中x0是D中一任给点,{αn},{β}是区间[0,1]中满足某些限制的实数列.Let E be a real Banach space with uniform normal structure, whose norm is uniformly Gateaux differentiable. Let D be a nonempty bounded closed convex subset of E and T : D → D be an asymptotically nonexpansive mapping. It is shown that under some suitable conditions, the sequence {xn} defined by the modified Reich-Takahashi iteration method (1.2) converges strongly to a fixed point of T, where x0 is any given point in D, and {αn}, {β} are real sequences in [0,1] with some restrictions.

关 键 词：不动点 渐近非扩张映象 修正的Reich-Takahashi迭代法 

分 类 号：O177.91[理学—数学]