Banach空间中的逼近问题

On the Approximation Problem in Banach Spaces

设E为实Banach空间,C为E上的非空闭凸子集且为E上的收缩核,P:E→C的保核收缩映象,文章在文献[2]的基础上,对带误差的迭代序列进行了修改,并证明了序列{xn}收敛于T1,T2,…,TN的公共不动点的充分必要条件为:limn→∞inf d(xn,F)=0,最后给出了在此基础上的两个推论.

Let E be a real Banach space, C is a nonempty closed convex subset of E and be a retract of E.A mapping P from E to C is a retraction.This paper, based on the [2] reference in the literature, removes the error of iterative sequences change and proves that the sequence {xn } converges stronglywith a common fixed point of T1, T2,……, Tu , if and only if lim inf d （x, F） = 0. Finally it presents two inferences on the basis of the corollary.