非自渐近非扩张映象的Reich-Takahashi型迭代法的强收敛定理  

Strong Convergence Theorems of the Modified Reich-Takahashi Iteration Method for Nonself Asymptotically Nonexpansive Mappings

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：《应用泛函分析学报》2007年第2期186-192,共7页Acta Analysis Functionalis Applicata

基　　金：宜宾学院自然科学基金(2006Z07)

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的非空闭凸子集而且是E的非扩张收缩核.设T:D→E是具有序列{kn}[1,∞),limn→∞kn=1的非自渐近非扩张映象,P:E→D是一非扩张保核收缩.本文证明了,在一定条件下,由修正的Reich-Takahashi迭代法(1.2)和(1.3)式定义的迭代序列{xn}强收敛于非自渐近非扩张映象T的不动点.Let E be a real Banach space with a uniformly Gateaux differentiable norm, D be a nonempty closed convex subset of E which is also a nonexpansive retract of E. Let T：D → E be a nonself asymptotically nonexpansive mapping with a squence {kn} belong to [1,∞）,kn → 1,P：E → D be a nonexpansive retraction of E onto D. It is shown that under some suitable conditions, the sequence {xn} defined by the modifed Reich-Takahashi iteration method （1- 2） and （1.3） converges strongly to a fixed point of T.

关 键 词：非自渐近非扩张映象 Reich—Takahashi迭代序列 不动点 

分 类 号：O177.91[理学—数学]