扰动压缩条件的点列收敛性问题  

The Point Range Convergence Problem in the Disturbed Compressibility Condition

作　　者：欧阳俊 张君[2] 

机构地区：[1]邵阳市教育局数学教研室,湖南邵阳422000 [2]邵阳学院资产管理处,湖南邵阳422000

出　　处：《邵阳学院学报（自然科学版）》2008年第3期4-6,共3页Journal of Shaoyang University：Natural Science Edition

摘　　要：本文研究完备度量空间X中满足ρ(xn,xn+1)≤Lp(xn+1,xn)+εn的点列{xn}收敛性问题,其中L∈(0,1)为常数,εn非负是无穷小量称为扰动.文中的主要结论是:点列{xn}的收敛性由扰动εn决定,即当幂级数(∞∑(n=1))εnxn的收敛半径R>1/L时,点列{xn}收敛.特别地,当R>1时,点列收敛;而时,{xn}敛散性不能确定.This paper studies the convergence problem of point range in complete metric space {xn} in complete metric space X.{ xn } meets p （xn,xn＋1） ≤ Lp （xn＋1,xn）＋εn, among which is constant. When εn is non-negative and infinitesimal, it is called perturbation. The main conclusion of this paper is： The convergence of point range { xn } determined by perturbation εn, that is, when the convergenee radius of power series is R 〉I/L, the poln range { xn } is convergent. Especially, when R〉 1, point range is convergent; when R=1,the convergence and divergence of { xn } is uncertain.

关 键 词：柯西点列 扰动 完备度量空间 收敛性 

分 类 号：O171[理学—数学]