渐近非扩张映象具误差的迭代集合序列收敛问题

Convergent Problem of Iterative Set Sequence with Errors for Asymptotically Nonexpansive Mappings

采用带误差的Ishikawa迭代型点序列逼近的方法研究了Banach空间中渐近非扩张映象不动点的迭代逼近问题,在一般条件下,得到了迭代集合序列{Qn}强收敛于T的不动点集F(T)的充要条件.所得结果改进和发展了已知的研究结果.

In this paper leting be a Banach space and leting be a proximinal subset of, leting be asymptotically nonexpansive mappings, under geneal condition, it is proved that the tierative set sequence with errors converges strongly to the set of mapping. This paper mainly uses three lemmas and the method,which the belt error an Ishikawa iteration sequence approaches, to study the queation which is appoximative processe of iteration sequence with errors for asymptotically nonexpansive mappings in the Banach space. The obtained result is improved and some people＇s newest achievements have been developed.