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

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.