有限簇非扩张映象不动点的黏性逼近  

Viscosity Approximtion of Fixed Points for a Finite Family of Nonexpansive Mappings

作　　者：赵良才[1] 张石生[1,2] 

机构地区：[1]宜宾学院数学系,宜宾644000 [2]四川大学数学系,成都610064

出　　处：《应用数学学报》2008年第4期599-607,共9页Acta Mathematicae Applicatae Sinica

摘　　要：设E是一致光滑的Banach空间,C是E之一非空闭凸子集.设f:G→C是一压缩映象。T_1,T_2,…,T_n:C→G是一有限簇非扩张映象且∩ from i=1 to N(F(T_i)≠Ф).本文用黏性逼近方法证明了,由(1.4)式定义的迭代序列{x_n}强收敛于T_1,T_2,…,T_N的一公共不动点的充分必要条件.本文结果也推广和改进了最近一些人的最新结果.Let E be a uniformly smooth Banach space, C a closed convex subset of E. Let f ： C → C be a contractive mapping, T1, T2,…, TN be a finite family of nonexpansive N mappings of C into itself such that the set ∩i=1^N F（Ti） of common fixed points of T1, T2,…, TN is nonempty. It is shown by using viscosity approximation methods, some sufficient and necessary conditions for the iterative sequence {xn} defined by （1.4） converges strongly to a common fixed point of T1, T2,…, TN. The results presented in this paper extend and improve some recent results.

关 键 词：非扩张映象 公共不动点 正规对偶映象 黏性逼近 

分 类 号：O177.91[理学—数学]