无穷可数族非自射非扩张映象之公共不动点的带误差逼近问题

Approximation to Common Fixed Points of Infinite Countable Family of Nonexpansive Nonself-Mappings with Errors

设E具Geaux可微的严格凸的自反Banach空间,C是E的一非空闭凸子集.受姚永红等2007年文献[1]的启发,本文在此Banach空间框架下引进了一涉及无穷可数族非自射非扩张映象{Ti:C→E}∞i=1的含误差的显式迭代算法,并且在非常少的限制条件下证明了该迭代序列的强收敛于无穷可数族非自射非扩张映象的一公共不动点.这个强收敛结果将姚永红等2007年文献[1]获得的主要结果从自射非扩张映象推广到非自射非扩张映象,从显式迭代算法推广到考虑一定范围误差存在的显式迭代算法.

Let E be a strictly convex and reflexive Banach spaces with an uniformly Geaux differentiable norm,and C be a nonempty closed convex subset of E.Under the framework or the space E,the author introduces an explicit iteration with errors,involving an infinite countable family of nonexpansive nonself-mappings {Ti∶C→E}∞i=1,and proves under very mild conditions that the iterative sequence converges strongly to a common fixed point of {Ti}∞i=1.The strong convergence theorem extends the main result obtained by Yao-Yao-zhou [1] in 2007 from nonexpansive self-mappings into nonexpansive nonself-mappings,and from explicit iteration into explicit iteration with errors.