Banach空间中ψ-半压缩型映象不动点的迭代逼近

设X为实一致光滑Banach空间，K为X的非空凸子集满足K+KK.设T：K→K为有界ψ-半压缩映象.设{vn｝∞n=0｛vn｝∞n=0为K中的序列，{αn｝∞n=0，{βn}∞n=0为0，1]中的实数列满足 　　(i) 　　(ii)αn→0，βn→0,n→∞ 　　(iii) 　　对任意初值x0∈K，定义Ishikawa迭代序列{xn｝∞n=0如下： 　　 　　若｛Tyn｝有界，则｛xn｝强收敛于T的唯一不动点.由此导出一些相关的结果.

Iterative Approximation of Fixed Points of ψ-Hemicontractive Maps in Banach Spaces

Let X be a real uniformly smooth Banach space, K a nonempty subset of X such that K+KK. Let T:K→K be a bounded ψ-hemicontractive map. Let {un}∞n=0 and {vn}∞n=0 be two sequences in K and {αn}∞n=0 and {βn}∞n=0 be two real sequences in0,1)satisfying 　　(i) 　　(ii)αn→0, βn→0,n→∞ 　　(iii) For an arbitrary initial value x0 ∈K,define the Ishikawa iterative sequence {xn} ∞n=0 as follows: 　　 If {Tyn}is bounded, then{xn }converges strongly to the unique fixed point of T. Some related results are deduced.