In normed space with limited dimension and infinite dimensional Fréche space,unconditional convergence of series is equivalent with absolute convergence.
文中讨论了无穷维赋范线性空间中,级数的收敛、绝对收敛、条件收敛、无条件收敛、弱无条件收敛等概念之间的关系,且通过反例说明弱无条件收敛的级数未必收敛、无条件收敛的级数未必绝对收敛等重要结论。
It is discussed that the relations between the convergence, absolute convergence, weakly unconditional convergence and unconditional convergence and summability of an infinite series ∑∞n=1x_nin a Banach space X.
研究了Banach空间X中的级数∑∞n=1xn的收敛性、绝对收敛性、弱无条件收敛性、无条件收敛性与可和性等概念之间的关系,证明了:当X为一般Banach空间时,无条件收敛性与可和性是等价的;当X为Hilbert空间时,弱无条件收敛性、无条件收敛性及可和性是等价的;当X为数域时,无条件收敛性与绝对收敛性及可和性是等价的。
conditionally convergent double series
条件收敛的二重级数
Study on EPI Convergence and Weaker Condition of Function Sequence Convergence
EPI收敛与函数序列收敛弱化条件的研究
A Sufficient Condition about Convergence Uniform of Function and a Sufficient and Necessary Condition about Convergence of Positive Series;
函数列一致收敛的一个充分条件和正项级数收敛的一个充要条件
D(∧) Convergence Rate of Conditional Moments
D(∧)吸引场的条件矩的收敛速度
Weaker Condition of EPI Convergence--EPI Nesting;
epi收敛条件的弱化——epi嵌套
Under the New Condition the Convergence of Newton-Like Meihod;
在新条件下拟Newton迭代方法的收敛性
The Necessary Convergence Condition of integral from a to (+∞) f(x)dx;
再论integral from a to (+∞)f(x)dx收敛的必要条件
On the properties of Sum Function at the Condition of Semi - Convergence Uniform;
亚一致收敛条件下和函数的分析性质
The Convergence of Algorithm for Solving Nonlinear Equations under Weak Condition
弱条件下解非线性方程算法的收敛性
Convergence of Chebyshev method under mild differentiability conditions of the first derivative
弱一阶可微条件下Chebyshev迭代法的收敛性
Note on the convergence of AOR and 2PPJ iterative methods
预条件AOR和2PPJ迭代法收敛性的注记
A sufficient and necessary condition of the AOR iterative method for consistently ordered matrices
相容次序矩阵AOR迭代收敛的充要条件
Convergence theorems for USSOR iterative methods with the precondition (I+C_α)
预条件(I+C_α)的USSOR迭代法收敛性定理
Cauchy condition for convergence of a series
柯西级数收敛条件。
Proof of the Function Seies Convergence Uniform Theorem and Necessary and Sufficient Condition in General Integral Convergent;
函数项级数一致收敛定理的证明和广义积分收敛的充要条件
Under some inexact conditions, the convergence of inexact alternating direction method is proved too.
在一定的非精确条件下，算法的收敛性得以证明。
Necessary and Sufficient Conditions for Strong Convergence of Iterative Sequence of Asymptotical Pseudo-contraction Mapping;
渐近伪压缩映象的迭代序列强收敛的充要条件
Global convergence analysis of the proposed method is given.
并在通常条件下证明了方法的全局收敛性。