一致凸Banach空间非扩张映象Ishikawa迭代收敛定理

Convergence theorems of Ishikawa iterative sequences for nonexpansive mappings in a uinformly convex Banach space

设E是一致凸Banach空间X中非空闭凸集,T:E→E是具不动点的非扩张映象.只要求}满足某种限制,证明了Ishikawa迭代序列强弱},{tnkIshikawa代序列的参数{sn},{tn}的子列{snk收敛定理.同时,提出了近似Picard迭代的概念,突破了对参数的限制,并证明了Picard迭代收敛定理.

Let X be a univformly convex Banach space,E be a nonempty closed subset of X and be an nonexpansive mapping with fixed points.It is shown that only the subsequence of Ishikawa iterative parameters satisfy some restrications,the strong and weak convergence theorems for Ishikawa iterative process are proved.Meanwhile,the concept of approximate Picard iteration is put forward and its convergence theorems is proved.