逼近Banach空间中渐近非扩张映象的不动点

Approximating Fixed Points of Asymptotically Nonexpansive Mappings in Banach Spaces

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=tn Tn( sn Tnxn+ ( 1 - sn) xn) + ( 1 - tn) xn,弱收敛到 T的不动点 ,其中 {tn},{sn}是区间 [0 ,1 ]中满足某些限制的实数列 .

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 \${x\-n}\$ defined by the modified Ishikawa iteration process: \$\$x\-\{n+1\}=t\-nT\+n(s\-nT\+nx\-n+(1-s\-n)x\-n)+(1-t\-n)x\-n,\$\$converges weakly to a fixed point of \$T\$, where \${t\-n}\$ and \${s\-n}\$ are sequences in \ with some restrictions.