逼近非扩张非自映像不动点（英文）

设E是一致凸Banach空间,K是E中非空闭凸集且是一个非扩张收缩核,T：K→E是具非空不动点集F（T）：={x∈K：Tx=x}的非扩张映像.设{α_n},{β_n},{γ_n},{α′_n},{β′_n},{γ′_n}是0,1]中实数列满足α_n＋β_n＋γ_n=α′_n＋γ′_n＋γ′_n=1,对任意初值x_1∈K,定义{x_n}如下（ⅰ）如果对偶空间E＊具有Kadec-Klee性质,那么{x_n}弱收敛于T的某不动点x＊∈F（T）;（ⅱ）若T满足（A）条件,那么{x_n}强收敛于T的某不动点x＊∈F（T）.

Approximating Fixed Points of Non-self Nonexpansive Mapping

Let E be a uniformly convex Banach space and K a nonempty convex closed subset which is also a nonexpansive retract of E.Let T:K→E be a nonexpansive mapping with F(T):={x∈K:Tx=x}≠Φ.Let αn,βn,γn,α'n,β'n,γ'n be real sequences in0,1]such that αn+βn+γn=α'n+β'n+γ'n=l,starting from arbitrary x1∈K,define the sequence{xn}by{yn=P(α'nTxn+β'nxn+γ'nun)/xn+1=P(αnTyn+βnxn+γnun)with the restrictions ∑∞n=1γn<∞,∑∞n=1<∞.Then (i)If the dual E* of E has the Kadec-Klee property,then weak convergence of a{xn}to some x*∈F(T)is proved;(ii)If T satisfies condition(A),then strong convergence of{xn}to some x*∈F(T)is obtained.