Approximation to Common Fixed Points of Infinite Countable Family of Nonexpansive Nonself-Mappings with Errors
Rao Ruo-feng · College Mathematics · 2011
Let E be a strictly convex and reflexive Banach spaces with an uniformly Geaux 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.