渐近非扩张映射的迭代收敛定理

Strong Convergence of the Iterative Scheme for Asymptotically Nonexpansive Mapping

E是实Banach空间,其范数是一致G-可微的;K是E的非空闭凸子集,T:K→K是具有序列{kn}[1,∞},limn→∞kn=1的渐近非扩张映射.在一定条件下,讨论的迭代序列{xn}强收敛到T的1个不动点.

Let E be a real Banach space with a uniformly Gateaux differentiable norm,K be a nonempty closed convex subset of E and T：K→K be an asymptotically nonexpansive mapping with a sequence {kn}[1,∞},limn→∞kn=1.It is shown that under some suitable conditions,the sequence {xn} converges strongly to some fixed point of T.