The fundamental purpose of this paper is to point out main features and several sufficient conditions of continuous function becoming absolute continuous function, introduce and apply an important theorem.
所述内容对深刻理解绝对连续函数类具有重要意义。
The authors discuss the problem whether the condition in the definition of a reproducing kernel space can be weakened or not and obtaine two conclusions as follows:(1) The conditions, u(x) being a real continuous function in interval [a,b] and u′(x)∈L~2[a,b], can not deduce the conclusion that u(x) is an absolute continuous function in interval [a,b].
讨论再生核空间W12 [a,b]定义中的条件是否可以减弱的问题,得到下面的两个结论:(1)条件u(x)是[a,b]上实的连续函数且u′(x)∈L2 [a,b]不能推出u(x)是[a,b]上实的绝对连续函数; (2)再生核空间W12 [a,b]定义中的条件改为u(x)在[a,b]是连续函数或连续囿变函数,那么函数空间不再是再生核空间。
The paper gives the definitions of monotonic function,bounded variation function and absolute continuous function,and discusses the relationship of the three.
文章给出了单调函数、有界变差函数、绝对连续函数的定义并讨论了三者之间的关系。
By using Bojanic-Cheng s method and analysis techniques,the author studies the approximation properties of Bernstein-Kantorovich-Bézier Operator for some Absolutely continuous functions in the case of 0<α≤1 and α≥1 respectively.
利用经典的Bojanic-Cheng方法,结合分析技术,分别讨论了Bernstein-Kantorovich-Bézier算子在0<α≤1及α≥1时,对一类绝对连续函数的逼近。
The purpose of this paper is to investigate the rate of convergence of Bernstein-Bézier Operator for some absolutely continuous functions.
为了进一步了解它的理论及其逼近性质,研究了它对一类绝对连续函数的逼近。
Using Bojanic-Cheng\'s method and analysis techniques,the authors study the approximation properties of BS-Bézier Operators for some absolutely continuous functions.
利用经典的Bojanic-Cheng方法,结合分析技术,研究了BS-Bézier算子对一类绝对连续函数的逼近性质,得到比较精确的收敛阶估计。
In this paper,we give a definition Of absolutely continuous functions with three levels,get some relational results with absolutely continuous functions with two levels and with bounded variation functions with three levels.
定义了三级绝对连续函数，并指出了它与二级绝对连续函数及三级有界交差函数的联系。