关于非扩展映象的弱收敛定理

Weak Convergence Theorems for Nonexpansive Mappings

首先讨论一个由非扩展映象的有限族所定义的迭代格式,主要证明了:设E为满足Opial条件的一致凸的Banach空间,C是E的非空间凸子集,Fi:C→C(i=1,2,…,r)为有限非扩展映象,且∩ri=1F(Ti)非空,设x1∈C,迭代地定义序列{xn}如下:xn+1=Wnxn, n≥1.其中Wn(n=1,2,…)为由T1,T2,…,Tr生成的W＿映象.则{xn}弱收敛于T1,T2,…,Tr的共同不动点.

Introduce an iteration scheme given by finite nonexpansive mappings, we prove the main resulf as follows: Let E be a uniformly convex Banach with Opial's condition, C be a nonempty convex sabsct of E,( T_i:C→C(i=1,2,)...,r)be finite nonexpansive mappings, ∩~r_(i=1)F(T_i)≠. let x_1∈C, iterative scheme {x_n} definited as follow:x_(n+1)=W_nx_n,_n≥1.where W_n(n=1,2,...)are W-mappings gcnerated by T_1,T_2,...,T_r, them{x_n}converges weedly to the common fixed point of T_1,T_2,...,T_r.