有限个λ半压缩映象族的强收敛定理

The Strong Convergence Theorems for a Finite Family of λ-demicontractive Mappings

设E为一致光滑的Banach空间且是一致凸的,C为E中的非空闭凸子集,T1,T2,…,TN:C→C是λ半压缩映象且为L-Lipschitzian映象,λ∈(0,1),公共不动点集非空,并且存在一个映象T∈{Ti:i∈I}是半紧的。{xn}是由xn+1=(1-an)xn+anTnxn确定的迭代序列,Tn=Tn mod N。在对{an}的一定假设条件下,本文证明了{xn}强收敛于T1,T2,…,TN的一个公共不动点。

Let E be a uniformly smooth real Banach space which is also uniformly convex,C be a nonempty closed convex subset of E.Let T1,T2,…,TN:C→C be a λ-demicontractive mappings for some λ∈(0,1) and L-Lipschitzian mapping.The common fixed point set is non-empty,there exist T∈{Ti:i∈I} is demicompact,{xn}is the iterative sequence defined by xn+1=(1-an)xn+anTxn,Tn=Tn mod N.Under suitable condition on{an},this paper proves that {xn}converges strongly to a common fixed point of T1,T2,…,TN.