bounded sequence

Based on the view that the theorem of closed mested interval is an axiom, this paper deduces the essential limit of monotonic bounded sequence of number and the Dedekind theorem, and proves the general theorem of bull closed nested interval of real number.

以通常所说的闭区间套定理作为公理推出单调有界数列存在极限和Dedekind定理，并且证明了通常所说的实数满闭区间套定理。

Three Stage Functions of Bounded Variation in Sequence Space λ and Their Characteristics

序列空间λ-三级有界变差函数及其特征

Notes on the Bounded Variation Sequence and Its Characteristic

关于囿变数列及其特征的若干注记

The ∧-bounded variation functions on sequence spaces

叙列空间上的∧&有界变差函数

The bounded variation sequence is applied broadly.

囿变数列又称为有界变差数列，在函数论中有广泛的应用。

For a nonlinear system of ordinary differential equations, we construct an iterative sequence and prove that the sequence is bounded. Using the sequence, the approximate solution is obtained.

对于非线性微分方程组，构造了一个迭代序列，证明了迭代序列是有界的，利用迭代序列构造近似解的表达形式。

This paper points out that if a sequence of Jacobian approximation satisfies the bounded deterioration, the sequence generated from the quasi& Newton methods is no better than linear convergence.

本文指出当Jacobian近似满足有界退化性质时，由拟牛顿算法得到的迭代序列最多是线性收敛的。