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 共查询到19条相似文献,搜索用时 78 毫秒
1.
本文研究了Bernstein-Durrmeyer代数多项式倒数对非负连续函数在Orlicz空间中的逼近问题.利用光滑模和K-泛函等工具,获得了收敛速度的估计,所得的结果比Lp空间内的相应结果具有拓展的意义.  相似文献   

2.
多元Bernstein-Durrmeyer算子Lp逼近的Steckin-Marchaud型不等式   总被引:2,自引:0,他引:2  
本文给出多元Bernstein-Durrmeyer算子Lp逼近的Steckin-Marchaud型不等式,从该不等式得到多元Bernstein-Durrmeyer算子Lp逼近的特征刻划定理.  相似文献   

3.
球面带形平移网络逼近的Jackson定理   总被引:2,自引:0,他引:2  
盛宝怀 《数学进展》2006,35(3):325-335
研究了球面带型平移网络逼近阶用球面调和多项式的最佳逼近及光滑模的刻画问题.借助于球调和多项式的最佳逼近多项式和Riesz平均构造出了单位球面Sq上的带形平移网络,并建立了球面带形平移网络对Lp(Sq)中函数一致逼近的Jackson型定理.所得结果表明球面带形平移网络可以达到球调和多项式的逼近阶.  相似文献   

4.
单纯形上的Stancu多项式与最佳多项式逼近   总被引:8,自引:2,他引:6  
曹飞龙  徐宗本 《数学学报》2003,46(1):189-196
作为Bernstein多项式的推广,本文定义单纯形上的多元Stancu多项式.以最佳多项式逼近为度量,建立Stancu多项式对连续函数的逼近定理与逼近阶估计,给出Stancu多项式的一个逼近逆定理,从而用最佳多项式逼近刻划Stancu多项式的逼近特征.  相似文献   

5.
本文研究了连续函数的最佳逼近多项式的点态逼近性质.通过一个具体函数的连续模估计,得到最佳逼近多项式的点态逼近阶估计,并且存在连续函数使得最佳逼近多项式能够满足Timan定理.  相似文献   

6.
单隐层神经网络与最佳多项式逼近   总被引:7,自引:1,他引:6  
研究单隐层神经网络逼近问题.以最佳多项式逼近为度量,用构造性方法估计单隐层神经网络逼近连续函数的速度.所获结果表明:对定义在紧集上的任何连续函数,均可以构造一个单隐层神经网络逼近该函数,并且其逼近速度不超过该函数的最佳多项式逼近的二倍.  相似文献   

7.
葛彩霞 《应用数学》1999,12(1):47-49
本文研究三层前馈型神经网络的最佳逼近能力,我们证明以多项式函数为隐层神经元作用函数的三层前馈型神经网络,当隐层神经元的个数超过某个给定的界限时,网络的输入输出函数张成一有限维线性空间,从而它可以实现对C(K)的最佳逼近.并且猜测,对非多项式函数的作用函数,若神经元个数有限,则它不具有最佳逼近性质.  相似文献   

8.
多元КАНТОРОВИЧ多项式的逼近定理   总被引:1,自引:0,他引:1  
李落清 《数学杂志》1989,9(1):109-116
本文利用逼近转化原理,建立了多元多项式逼近的量化Korovkin型定理。改进和完善了[2]中的结果。  相似文献   

9.
本文引进了推广的Bernstein-Kantorvich多项式Mn^(κ)(αn,f,x)并且估计了它在空间Lp[0,1]中的逼近阶。  相似文献   

10.
分别讨论了以第二类Chebyshev多项式的零点、Jacobi多项式的零点、第一类Chebyshev多项式的零点为插值结点组的五类Kantorovich型插值算子在Orlicz空间内的逼近问题,得到了逼近阶的上界估计.  相似文献   

11.
研究Bernstein-Durrmeyer多项式的加权逼近并建立其饱和定理.  相似文献   

12.
In this paper, the order of simultaneous approximation and Voronovskaja kind results with quantitative estimate for complex Bernstein-Durrmeyer polynomials attached to analytic functions on compact disks are obtained. In this way, we put in evidence the overconvergence phenomenon for Bernstein-Durrmeyer polynomials, namely the extensions of approximation properties (with quantitative estimates) from real intervals to compact disks in the complex plane.  相似文献   

13.
As a generalization of the Bernstein-Durrmeyer operatora defined on the simplex, a class of general Bernstein-Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong direct theorem and an inverse theorem of weak type for these operators by using a decom-position way. From the theorems the characterization of Lp approximation behavior is derived.  相似文献   

14.
最近.许树声[1]撰文给出了对L_p范数下凸约束最佳逼近的特征定理.并研究了该定理的苦干应用.然而,文[1]引理1证明中部分地方有误.本文给予了纠正,予以重新证明  相似文献   

15.
In the present paper, we find that the Bemstein-Durrmeyer operators, besides their better applications in approximation theory and some other fields, are good tools in constructing translation network. With the help of the de la Vallee properties of the Bernstein-Durrmeyer operators a sequence of translation network operators is constructed and its degree of approximation is dealt.  相似文献   

16.
In 1967 Durrmeyer introduced a modification of the Bernstein polynomials as a selfadjoint polynomial operator on L2[0,1] which proved to be an interesting and rich object of investigation. Incorporating Jacobi weights Berens and Xu obtained a more general class of operators, sharing all the advantages of Durrmeyer’s modification, and identified these operators as de la Vallée-Poussin means with respect to the associated Jacobi polynomial expansion. Nevertheless, all these modifications lack one important property of the Bernstein polynomials, namely the preservation of linear functions. To overcome this drawback a Bernstein-Durrmeyer operator with respect to a singular Jacobi weight will be introduced and investigated. For this purpose an orthogonal series expansion in terms generalized Jacobi polynomials and its de la Vallée-Poussin means will be considered. These Bernstein-Durrmeyer polynomials with respect to the singular weight combine all the nice properties of Bernstein-Durrmeyer polynomials with the preservation of linear functions, and are closely tied to classical Bernstein polynomials. Focusing not on the approximation behavior of the operators but on shape preserving properties, these operators we will prove them to converge monotonically decreasing, if and only if the underlying function is subharmonic with respect to the elliptic differential operator associated to the Bernstein as well as to these Bernstein-Durrmeyer polynomials. In addition to various generalizations of convexity, subharmonicity is one further shape property being preserved by these Bernstein-Durrmeyer polynomials. Finally, pointwise and global saturation results will be derived in a very elementary way.  相似文献   

17.
关于函数及其导数用Bernstein-Durrmeyer算子的同时逼近   总被引:1,自引:0,他引:1  
郭顺生  刘喜武 《数学学报》2000,43(2):367-374
本文利用点态连续模研究了Bernstein-Durrmeyer算子的同时逼近,推广了关于有界变差函数和连续函数的结果.  相似文献   

18.
修正的Bernstein-Durrmeyer算子的同时逼近   总被引:1,自引:0,他引:1  
本文的目的是证明修正的Bernstein-Durrmeyer算子同时逼近的正逆定理,在点态意义下,我们得到了一个同时逼近的等价特征刻画。  相似文献   

19.
As a generalization of the Bernstein-Durrmeyer operators defined on the simplex, a class of general Bernstein-Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong direct theorem and an inverse theorem of weak type for these operators by using a decomposition way. From the theorems the characterization of L^p approximation behavior is derived  相似文献   

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