逼近非扩张非自映像不动点(英文)

Approximating Fixed Points of Non-self Nonexpansive Mapping

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).

Let E be a uniformly convex Banach space and K a nonempty convex closed subsetwhich is also a nonexpansive retract of E.Let T：K→E be a nonexpansive mapping withF（T）：= {x∈K：Tx = x}≠Φ.Let α_n,β_n,γ_n,α_n＇,β_n＇,γ_n＇ be real sequences in[0,1]such thatα_n ＋β_n ＋γ_n =α_n＇＋β_n＇＋γ_n＇= 1,starting from arbitrary x_1∈K,define the sequence {x_n} bywith the restrictionsγ_n∞,γ_n＇∞.Then（i） If the dual E~＊ of E has the Kadec-Klee property,then weak convergence of a {x_n} to somex~＊∈F（T） is proved;（ii） If T satisfies condition（A）,then strong convergence of {x_n} to some x~＊∈F（T） is obtained.