Banach空间中间意义下的渐近k-严格伪压缩映象不动点的迭代逼近

Approximation of Fixed Points of Asymptotically k-strict Pseudocontractive Mapping in the Intermediate Sense in Banach Space

设E是实Banach空间,C是E的非空闭凸子集,T:C→C是一致L-Lipschitz的中间意义下的渐近k-严格伪压缩映象且∑∞n=1γn<∞,任取一点x0∈E,{xn}是根据xn+1=(1-αn-βn)xn+αnTnxn+βnun定义的具误差的修改的Mann迭代序列,若F(T)非空有界,在对参数的一些适当限制条件下,得到了{xn}强收敛于T的一个不动点的充要条件是lim infn→∞D (xn,F(T))=0;去掉F(T)有界的条件后对参数进行同样的限制,得到了根据xn+1=(1-αn)xn+αnTnxn定义的修改的Mann迭代序列{xn}强收敛于T的一个不动点的充要条件是lim infn→∞D (xn,F(T))=0。

Let E be a real Banach space and C be a nonempty closed convex subset of E. T： C→C is a uniformly L-Lipscbitz as-ymptotically k-strict pseudocontractive mapping in the intermediate sense andE be any given point,the modified Mann iterative sequence with errors defined byis nonempty andbounded, under some appropriate restricted conditions, a necessary and sufficient condition for {xn} converges strongly to a fixedpoint of T is lira inf E After removing the condition that F（T） is hounded, under the same restricted conditionson the parameters, the modified Mann iterative sequence {xn } defined byconverges strongly to a fixedpoint of T if and only if lim in D（xn, F（T） ） =0