非扩张映像Ishikawa迭代参数趋向[0,1]端点时的收敛定理  

Ishikawa Iteration Convergence Theorems for Nonexpansive Mappings when Parameter Approximate End Point of [0,1]

作　　者：顾光辉[1] 苏永福[2] 

机构地区：[1]沧州师范专科学校数学系,河北沧州061001 [2]天津工业大学理学院,天津300160

出　　处：《河北师范大学学报（自然科学版）》2005年第3期224-227,共4页Journal of Hebei Normal University：Natural Science

基　　金：天津市学科建设基金资助项目(100580204)

摘　　要：设X是一致凸Banach空间,C是X中非空闭凸子集,T:C→C是具不动点的非扩张映像,对任意的x1∈C,存在Ishikawa迭代过程{xn}(xn+1=(1-tn)xn+tnT(snTxn+(1-sn)xn),tn→1,sn→0,∑∞‖→0(k→∞).证明了当映像T具紧性时,Ishikawa迭(1-tn)=+∞)的子序列{xnk},使‖xnk-Txnkn=1代过程{xn}强收敛于某不动点,当空间X满足Opial's条件时,Ishikawa迭代过程{xn}弱收敛于某不动点.Let X be a uniformly convex Banach space and C be a nonempty colsed convex subset of X,and T:C→C be a nonexpansive mapping,for x_1∈C and {s_n},{t_n}[0,1],exsits subsequence{x_(n_k)}of x_(n+1)=(1-t_n)x_n+t_nT(s_nTx_n+(1-s_n)x_n),t_n→1,s_n→0,∑∞n=1(1-t_n)=+∞, such that‖x_(n_k)-Tx_(n_k)‖→0(k→∞),if T is compact then Ishikawa iterative process {x_(n_k)}converges strongly to a fixed point,if X satisfies Opial's condition then Ishikawa iterative process {x_(n_k)}converges weakly to a fixed point.

关 键 词：非扩张映像 ISHIKAWA迭代过程 迭代参数 收敛定理 一致凸BANACH空间 端点 不动点 闭凸子集 子序列 强收敛 弱收敛 sn 紧性 

分 类 号：O177.91[理学—数学] O175.25[理学—基础数学]