渐近非扩张映射修正的Ishikawa迭代程序收敛定理  

Convergence Theorem of Modified IshikawaIterative Sequences for Asymptotically Nonexpansive Mappings

作　　者：郭志荣[1] 徐小平[2] 

机构地区：[1]扬州职业大学数学系 [2]南通职业大学基础部

出　　处：《淮阴师范学院学报（自然科学版）》2010年第5期377-381,共5页Journal of Huaiyin Teachers College;Natural Science Edition

基　　金：国家自然科学基金资助项目(10571150)

摘　　要：主要在E*具有KK性质等条件下证明了T存在不动点当且仅当由修正的Ishikawa迭代程序xn+1=tnTnyn+(1-tn)xn yn=snTnxn+(1-sn)xn所定义的序列{xn}弱收敛且xn-Txn→0.设C是一致凸Banach空间E的非空有界闭凸子集,T:C→C是渐近非扩张映射.Let C be a nonempty bounded closed convex subset of uniformly convex Banach space.Let T：C→C be an asymptotically nonexpansive mapping.It is shown that under some suitable conditions such as thatE＊ satisfies KKproperty,Thas fixed point if and only if the modifiedIshikawaiterative sequences {xn}defined by xn＋1=tnTnyn＋（1-tn）xn yn=snTnxn＋（1-sn）xn converges weakly and xn-Txn→0.

关 键 词：BANACH空间 渐近非扩张映射 ISHIKAWA迭代 Kadec-Klee性质 

分 类 号：O177.2[理学—数学]