Banach空间中渐近伪压缩映射的黏滞近似不动点序列

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.

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

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+λnTnxn,for n≥1,where {λn},{θn}(0,1) are real sequences and satisfy some conditions.Then ‖xn-Txn‖→0,as n→∞.