一致凸Banach空间渐近非扩张映像Ishikawa迭代收敛定理

Convergence theorems of Ishikawa iterative for asymptotically nonexpansive mapping in a uniformly convex Banach spaces

关于一致凸Banach空间中渐近非扩张映像的迭代收敛定理,刘启厚等推广了Jurgenschu的结果,得到了有界闭凸集上渐近非扩张映像Ishikawa迭代收敛定理.本文得到了闭凸集上渐近非扩张映像Ishikawa迭代收敛定理,并减弱了参数条件.

The relative result of Jurgen schu is extended to a uniformly convex Banach space, and the convergence of iterative sequence in an uniformly convex Banach space for asymptotically nonexpanstive mapping is proved by LiuQihou and LiXia, T is asymptotically nonexpanstive mapping with sequence{Kn}in a bounded closed convex subset C of uniformly convex Banach space. In this paper, we let only C is closed convex subset of uniformly convex Banach space.But convergence theorems of iterative sequences for asymptotically nonexpanstive mapping is also proved.