渐近非扩张映像公共不动点复合隐格式迭代算法

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

提出了Banach空间中渐近非扩张映像族{Ti}Ni=1公共不动点复合隐迭代格式:xn=anxn-1+(-an)Tnnyn,yn=βxn-1+(1-bn)Tnnxn,其中Tn=TnmodN,证明了弱收敛和强收敛定理,其结果推广和改进了Xu和Ori(2001),Oilike(2004),周海云和张石生教授(2002)及其他作者的结果。

：This paper introduce the following composite implicit iteration schemes：{^xn=αnxn-1＋（1-αn）T^nnyn yn=βnxn-1＋（1-βn）T^nnxn where Tn=Tn mod N, for common flxcd points of a finite family of asymptotically nonexpansive mappings {Ti}^Ni=i in Banach spaces. This paper also prove some weak and strong convergence theorems. The results presented in this paper extend, generalize and improve the results of Xu, Ori, Oilike ,Chang and other authors.