摘要
设E是一致凸Banach空间,满足Opial条件或具有Frechet可微范数.又设C是E的有界闭凸子集.若T:C→C是非扩张映象,则对任给的初始数据x0∈C,由Ishikawa迭代程序定义的序列{xn}弱收敛到T的不动点,其中,{tn},{sn}是区间[0,1]中满足某些限制的序列.
Let E be a uniformly convex Banach space which satisfies Opial’s conditionor has a Frechet differentiable norm.and C be a bounded closed convex subset of E.IfT:C→C is a nonexpansive mapping.then for any initial data x0∈C,the Ishikawaiteration process{xn},defined by xn=tnT(snTxn+(1-sn)xn)+(1-tn)xn,n≥0,converges weakly to a fixed point of T,where{tn}and{sn}are sequences in[0,1]withsome restrictions.
基金
Supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE,China.
关键词
非扩张映象
不动点逼近
ISHIKAWA迭代程序
fixed point
nonexpansive mapping
Ishikawa iteration process
uniformly convex Banach space.
