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：刘水凤[1] 张君[1] 陈继业[1] 刘水强[1] 

机构地区：[1]邵阳学院数学与计算科学研究所,湖南邵阳422000

出　　处：《大学数学》2009年第5期173-176,共4页College Mathematics

基　　金：湖南省科技计划资助项目(07CK3014);湖南省教育厅重点资助项目(06A066);湖南省教育厅科研(06C753)

摘　　要：研究完备度量空间X中满足ρ(xn,xn+1)≤Lρ(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sum from n=1 to ∞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R=1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 L∈ （0,1） 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 convergence radius of power series is R〉1/L, the point 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]