Banach空间中修正的Reich-Takahashi迭代法的强收敛性

Strong convergence theorems of the modified Reich-Takahashi iteration method in Banach spaces

设E是一实的p-一致光滑的B anach空间(1<p≤2),D是E的非空闭凸子集而且是E的非扩张收缩核.设T∶D→E是具有序列{kn}[1,∞),limn→∞kn=1的非自渐近非扩张映象,P∶E→D是一非扩张保核收缩.本文证明了在一定条件下,由修正的R e ich-Takahash i迭代法(1)和(2)式定义的迭代序列{xn}强收敛于非自渐近非扩张映象T的不动点.

Let E be a real p - uniformly smooth Banach space （ 1 〈 p ≤ 2 ）, D be a nonempty closed convex subset of E, which is also a nonexpansive retract of E. Let T ： D→E is a nonself asymptotically nonexpansive mapping with a sequence { kn } 包含 [ 1, ∞ ）, limn→∞kn=1, P ： E→D be a nonexpansive retraction. It is shown that under some suitable conditions, the sequence {xn} defined by the modified-Reich- Takahashi iteration method（ 1 ）and（2）converges strongly to the f＇rxed point of nonself asymptotically nonexpansive mapping T.