扰动压缩条件的点列收敛性问题

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.

The Point Range Convergence Problem in the Disturbed Compressibility Condition

This paper studies the convergence problem of point range in complete metric space {xn} in complete metric space X.{xn} meets ρ(xn,xn+1)≤Lρ(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.