有限个非扩张非自映像隐迭代格式的逼近

Strong Convergence of an Implicit Iteration for a Finite Family of Non-self Nonexpansive Mappings

假设E为一致凸Banach空间,K为E的非空闭凸子集且为E的非扩张收缩,P为非扩张收缩映像.{Ti:i=1,2,…,N}:K→E为非扩张映像且F(T)=∩ from i=1 to N F(Ti)≠■.定义{xn}如下:x0∈K,xn=P(αnxn-1+(1-αn)TnP[βnxn-1+(1-βn)Tnxn]),n≥1,这里{αn},{βn}为[δ,1-δ]中的实序列,其中δ∈(0,1).若{Ti:i=1,2,…,N}满足条件(B),则{xn}强收敛于x*∈F(T).

Suppose K is a nonempty closed convex nonexpansive retract of a uniformly convexBanach space E with P as a nonexpansive retraction.Let {Ti：i=1,2,…,N}：K→E be N nonexpansive mappings with F（T）=∩^N i=1 F（Ti）≠0. Define a sequence {xn} as follows; x0∈K,xn=P（αnxn-1＋（1-αn）TnP[βnxn-1＋（1-βn）Tnxn]）,n≥1,where{αn},{βn}are real sequences in [δ,1-δ]for some δ∈（0,1）.If{Ti：i=1,2…,N} satisfy the condition （B）, the strong convergence of （xn} to some point x^＊ ∈ F（T） is obtained.