广义复合隐迭代格式逼近非扩张映像公共不动点

摘要

The purpose of this paper is to introduce the following general composite implicit iteration schemes:{ xn = αnxn-1 + (1 - αn)Tnyn,yn = rnxn + snxn-1 + tnTnxn + wnTnxn-1,rn + sn + tn + wn= 1,{αn},{rn},{sn},{tn},{wn} ∈ [0,1],where Tn = Tn mod N, for common fixed points of a finite family of nonexpansive mappings {Ti}iN=1 in Banach spaces, and to prove weak and strong convergence theorems. The general composite implicit iteration scheme presented in this paper included various concrete iteration schemes. Hence , the results presented in this paper extend, generalize and improve the results of Mann, Ishikawa, Xu and Ori, and other authors.%提出并使用如下广义复合隐迭代格式逼近非扩张映像族{Ti}Ni=1公共不动点:xn=αnxn-1+(1-αn)Tnyn,yn=rnxn+snxn-1+tnTnxn+wnTnxn-1,rn+sn+tn+wn=1,{αn},{rn},{sn},{tn},{wn}∈[0,1],这里Tn=Tn mod N.该文提出的广义复合隐迭代格式包含了目前多种迭代格式,因此,所得强弱收敛定理推广及发展了Mann,Ishikawa,Xu and Ori,等许多作者的结果.