广义复合隐迭代格式逼近非扩张映像公共不动点(英文)

General Composite Implicit Iteration Processes for Common Fixed Points of a Finite Family of Nonexpansive Mappings

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=TnmodN.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,XuandOri,等许多作者的结果.

The purpose of this paper is to introduce the following general composite implicit iteration schemes ：{X=anxn-1＋（1-an）Tnyn,yn=rnxn＋snxn-1＋tnTnxn＋wnTnxn-1,rn＋sn＋tn＋wn=1,{an},{rn},{sn},{tn},{wn}∈[0,1] where Tn= Tn, mod N, for common fixed points of a finite family of nonexpansive mappings {Ti}i^N=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.