On the problem of nearest common fixed point of nonexpansive mappings

Abstract

本文在Hilbert空间的框架下,研究无限族非扩张映象T1,T2,…的迭代程序xn+1=λn+1y+(1-λn+1)Tn+1xn的收敛性问题．在适当的条件下,证明了该迭代序列收敛于这一非扩张映象族的最近的公共不动点．其结果改进和推广了引文中相应的结果． The purpose of this paper is to study the convergence problem of the iteration scheme xn+1=λn+1y+（1-λn+1）Tn+1xn for a family of infinitely many nonexpansive mappings T1,T2,...in a Hilbert space.It is proved that under suitable conditions this iteration scheme converges strongly to the nearest common fixed point of this family of nonexpansive mappings.The results presented in this paper extend and improve the corresponding results.