Convergence Theorms of Ishikawa Iterative for Asymptotically Non—expansive Mapping in a Uniformly Convex Banach space

文［４］把文［３］的主要结果从 Ｈｉｌｂｅｒｔ空间推广到一致凸Ｂａｎａｃｈ空间，证明了一致凸 Ｂａｎａｃｈ空间 上从有界闭凸集到自身的渐近非扩张映象的迭代序列收敛定理。本文将有界闭凸集的条件减弱为闭 凸集，从而推广了文［４］的相应结果。

In paper [4], the relative result of Jiirgen schu is extended to a uniformly con- vex Banach space, and the convergence of iterative sequence in an uniformly conves Banach space for asymptotically non-expanstive mapping is proved. In paper [4], T is asymptotically non-expanstive mapping with sequence {Kn} in a bounded closed convex subset C of uniformly convex Banach space. In this paper, we let only C is closed convex subset of uniformlly convex Ba- nach space. But convergence theorms of iterative sequences for asymptotically non-expanstive mapping was also proved.