Banach空间中非扩张映射的不动点逼近的Ishikawa迭代程序

Approximating Fixed Points of Nonexpansive Mapping by Ishikawa Iteration Process in Banach Space

设X为实一致凸Banach空间,其共轭空间X*具有KK性质,C为X的非空有界闭凸子集。若T为C到自身的非扩张映射,则对任给的x0∈C,Ishikawa迭代程序xn+1=tnT(snTxn+(1-sn)xn)+(1-tn)xn,n=0,1,2,…,定义的序列{xn}弱收敛到T的某个不动点,其中{tn},{sn}满足一定的条件。

Let X be a uniformly convex Banach space, whose dual space X^＊ has the KK property. Let C be a bounded closed convex subset of X. Let T： C to C be a nonexpansive mapping. It is shown that for any initial guess x0∈ C , the Ishikawa iteration / xo t defined by xn＋1=tnT（snTxn＋（1-sn）xn）＋（1-tn）xn,n=0,1,2,…, converges to a fixed points of T weakly, where {tn},{sn} are sequence in [ 0, 1 ] with certain restrictions.