关于渐近非扩张映象不动点迭代的一点注记

A Note on Approximating Fixed Points of Asymptotically Nonexpansive Mapping

设E是一致凸Banach空间,C是E的非空闭凸子集,T:C→C是具有不动点的渐近非扩张映象．该文证明了在某些适当的条件下,由下列修改了的Ishikawa迭代程序所定义的序列{xn}=xn+1=rpn,pn=(1-an)xn+anTmn ryn+un,yn=(1-bn)xn+bnTkn xn+vn, (n≥1)弱收敛到t的不动点．

Let E be a uniformly convex Banach space, C be a nonempty closed convex subset of E, and T ： C → C be an asymptotically nonexpansive mapping with fixed points. It is shown that under some suitable conditions, the sequence {xn} defined by the modified Ishikawa iteration process： {xn}：xn＋1=rpn,pn=（1-αn）xm＋αmT^mn ryn＋un,yn=（1-bn）xn＋bnT^knxn＋vn,（n≥1） converges weakly to a fixed point of T.