有限簇非扩张映象具误差的黏性逼近

Viscosity Approximtion of Fixed Ponts for Finite Family of Nonexpansive Mappings

设E是一致光滑的Banach空间,C是E之一非空闭凸子集.设f∶C→C是一压缩映象,T1,T2…,TN∶C→C是一有限簇非扩张映象且∩iN=1F(Ti)≠θ.设序列{xn}定义为xn+1=αnf(xn)+(1-αn-γn)Tnxn+γnun.本文用黏性逼近方法证明了,在一定条件下,序列{xn}强收敛于T1,T2…,TN的一公共不动点.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 mappings of C into itself such that the set ∩ i^N=1 F（Ti） of common fixed points of T, ,T2..-, TN is nonempty. Let the sequence { xn } be defined by xn＋1=anf（xn）＋（1-an-yn）Tnxn＋ynun. It is shown by using viscosity approximation methods that under some suitable conditions the sequence { xn } converges strongly to a common fixed point of T1 ,T2... ,TN. The results presented in this article also extend and improve some recent results.