Banach空间中渐近伪压缩映射的黏滞近似不动点序列  

Viscosity Approximate Fixed Point Sequence for Asymptotically Pseudo-contractive Mapping in Banach Spaces

作　　者：魏利[1] 谭瑞林[1] 周海云[2] 

机构地区：[1]河北经贸大学数学与统计学学院,河北石家庄050061 [2]军械工程学院陆学与应用数学研究所,河北石家庄050003

出　　处：《数学的实践与认识》2010年第1期166-171,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10771050);河北省教育厅科学研究计划项目(2009115)

摘　　要：首先给出了渐近伪压缩映射的黏滞近似不动点序列的新定义,继而证明了如下逼近定理:令K为实Banach空间E的非空闭凸有界子集,T:K→K为一致L-Lipschitz、具数列{εn}的一致渐近正则、具数列{kn}的渐近伪压缩映射.假设迭代序列{xn}定义为:x1∈K,对n≥1,xn+1:=λnθnf(xn)+[1-λn(1+θn)]xn+λnTnxn,其中{λn},{θn}(0,1)且满足一定条件,则:当n→∞时,‖xn-Txn‖→0.The new definition of viscosity approximate fixed point sequence of asymptotically pseudo-contractive mapping is first introduced ,then an approximate theorem is proved. Suppose K is a nonempty closed convex and bounded subset of a real Banach space E,T ： K → K is a uniformly L-Lipschitz, asymptotically pseudo-contractive with constant {kn} and uniformly asymptotically regular with constant {εn},Let{xn}be generated from x1 ∈ K by xn＋1：=λnθnf（xn）＋[1-λn（1＋θn）]xn＋λnT^nxn,for n≥1,where {λn},{θn}（∪↓）（0,1）are real sequences and satisfy some conditions.Then｜｜xn-Txn｜｜→0,as n→∞.

关 键 词：渐近伪压缩映射 近似不动点序列 一致渐近正则映射 强收敛 

分 类 号：O177.2[理学—数学]