严格伪压缩映像隐迭代格式逼近公共不动点的几何结果  

Geometric Results for Implicit Iteration Process Approximating Common Fixed Points of Strictly Pseudocontractive Mappings

作　　者：苏永福[1] 顾光辉[2] 

机构地区：[1]天津工业大学理学院,天津300160 [2]沧州师范专科学校数学系,河北沧州061001

出　　处：《河北大学学报（自然科学版）》2005年第5期458-460,共3页Journal of Hebei University(Natural Science Edition)

基　　金：天津市学科建设基金资助项目(100580204)

摘　　要：设K是Hilbert空间E中非空闭凸集,Ti∶K→K是具不动点集F(Ti)的严格伪压缩映像,且F=∩1≤i≤NF(Ti)≠φ,i=1,2,3,…,N.对x0∈K与{αn}[0,1],隐迭代格式{xn}定义为xn=αnxn-1+(1-αn)Tnxn,n≥1.这里Tn=TnmodN,如果{xn}收敛于Ti的公共不动点p∈F,i=1,2,3,…,N,且xn≠p,则对任意y∈F,有li msupn→+∞(y-p,‖xxnn--pp‖)≤0.称这一几何结果为逼近不动点的钝角原理.Let K be a nonempty closed convex subset of Hilbert space E, Ti ： K→K, i = 1,2,3,…, N, are strictly Pseudocontractive Mappings such that the common set of fixed points F = ∩ 1≤i≤NF（ Ti ）≠ Ф. Let x0 ∈ K and an（0,1）, the implicit iteration sequence{ xN } defined by xn=anxn-1＋（1-an）Tnxn,n≥1. whrer Tn = TnmodN, if { xn } converges to a common fixed point p of the mappings Ti, i = 1,2,3, …, N, and xn ≠ p, then for and y ∈ F, the following holds lim sup n→∞（y-p,xn-p/‖xn-p‖）≤0.

关 键 词：Hilbter空间 严格伪压缩映像 隐迭代格式 逼近不动点 几何结果 

分 类 号：O177.91[理学—数学]