有限个严格压缩映像隐迭代格式的逼近(英文)

Convergence Theorems of an Implicit Iteration for a Finite Family of Strictly Pseudo-contractive Mappings

假设E为一致凸的Banach空间,对偶空间E*有Kadec-Klee性质,K为E的非空闭凸子集{Ti:i=1,2,…,N}:K→K为Browder-Petryshyn意义下的严格伪压缩映像且F=∩Ni=1F(Ti)≠0.{αn}n∞=1满足0<aαnb<1.定义Si=(1-δ)I+δTi(i=1,2,…,N),这里I代表恒等映像而δ∈(0,1).定义{xn}如下xn=αnxn-1+(1-αn)Snxn,n1,这里Sn=Sn(modN).则{xn}弱收敛于{Si}Ni=1的公共不动点.

Suppose E is a uniformly property. Let K be a nonempty closed convex convex Banach space and its dual space E^＊ has Kadec-Klee subset of E and Ti ：K → K （i = 1,2,… ,N） be strictly N pseudo-contractive mappings in the terminology of Browder-Petryshyn such that F = ∩i=1^N F（Ti） ≠Ф, and let {αn}n=1^∞ be a sequence satisfying the conditions 0 〈 a ≤ a≤ b 〈 1. Define mappings Si = （1 - δ）I ＋ δTi （i = 1,2, …… ,N）, wbere I denotes the identity mapping. Let x0 E ∈ and {xn} be defined by xn=anxn -1 ＋ （1-an）Snxn ,n≥ 1, where Sn = Sn（modN）. Then {xn} converges weakly to a common fixed point of mappings {Si}i=1^N.