d维Bernstein算子加Jacobi权的收敛阶

１．引 言 设Ｓ＝Ｓｄ（ｄ＝１,２,…）是 Ｒｄ中的单纯形,即记ｋ＝（ｋ１,ｋ２,……,ｋｄ）∈Ｒｄ,ｋｉ为非负整数, ,则Ｓ上定义的函数ｆ所对应的ｄ维Ｂｅｒｎｓｔｅｉｎ算子定义为其中 Ｐｎ,ｋ（ｘ）＝是 Ｂｅｒｎｓｔｅｉｎ基函数．引进多维Ｊａｃｏｂｉ权函数, 这里 ．定义Ｂｅｒｎｓｔｅｉｎ权函数 表示微分算子． 记 是单位向量,即第ｉ个分量为１,其余ｄ－１个分量为０, ．定义函数ｆ在方向ｅ上的ｒ阶对称差分为Ｃ（Ｓ）中的加权Ｓｏｂｏｌｅｖ空间为其中Ｓ为Ｓ的内部．定义加权Ｋ－泛函及加权光滑模其中 为加权范数． …     

关于Bernstein多项式的绝对收敛性

该文研究Ｂｅｒｎｓｔｅｉｎ多项式的绝对收敛性．证明了，对每个ｘ∈［０，１］，一个有界变差函数的Ｂｅｒｎｓｔｅｉｎ多项式序列是绝对｜Ｃ，１｜可和的，而且给出了Ｂｅｒｓｔｅｉｎ多项式序列的绝对｜Ｃ，１｜和式的余项的估计．     

多元Bernstein多项式加权逼近的Steckin-Marchaud型不等式

引进一种新的光滑模,建立多元Ｂｅｒｎｓｔｅｉｎ多项式加权逼近的Ｓｔｅｃｋｉｎ Ｍａｒｃｈａｕｄ型不等式．     

Bernstein-Sikkema算子逼近

研究Ｂｅｒｎｓｔｅｉｎ－Ｓｉｋｋｅｍａ算子的逼近问题,得到强型正定理和弱型逆定理,改进了文献［１］的结果     

关于Sikkema－Bernstein算子的导数逼近

关于Ｓｉｋｋｅｍａ－Ｂｅｒｎｓｔｅｉｎ算子的导数逼近徐淳宁，何甲兴（长春邮电学院，１３００１２）（吉林工业大学，长春１３００２５）设ｆ定义在［０，１］上，ｆ的Ｂｅｒｎｓｔｅｉｎ算子如下ｃｈｅｎｇ在［１］中研究了Ｂ（ｆ，ｘ）对有界变差函数的逼近阶，郭顺...     

Bernstein－Sikkema算子的正逆定理

本文给出了Ｂｅｒｎｓｔｅｉｎ－Ｓｉｋｋｅｍａ算子的一个积分型估计式以及一个弱性逆定理     

Bernstein—Sikkema算子的正逆定理

本文给出了Ｂｅｒｎｓｔｅｉｎ－Ｓｉｋｋｅｍａ算子的一个积分型估计式以及一个弱性逆定理。     

单纯形上Bernstein多项式的迭代极限

单纯形上Ｂｅｒｎｓｔｅｉｎ多项式的迭代极限陈发来（中国科学技术大学数学系，合肥２３００２６）ＬＩＭＩＴＯＦＩＴＥＲＡＴＥＳＦＯＲＢＥＲＮＳＴＥＩＮＰＯＬＹＮＯＭＩＡＬＳＤＥＦＩＮＥＤＯＮＡＳＩＭＰＬＥＸ￥ＣＨＥＮＦＡＬＡＩ（ＤｅｐａｒｔｍｅｎｔｏｆＭ...     

广义Bernstein─Bezier多项式的若干性质

本文研究了广义Ｂｅｒｎｓｔｅｉｎ—Ｂéｚｉｅｒ多项式的某些性质，从而说明了广义Ｂｅｒｎ－ｓｔｅｉｎ─Ｂｅｚｉｅｒ多项式与所逼近所函数保持着相近的性质。     

Bernstein-Bezier Surface Patches on Arbitrary Spatial Triangulation

Ｂｅｒｎｓｔｅｉｎ－ＢéｚｉｅｒＳｕｒｆａｃｅＰａｔｃｈｅｓｏｎＡｒｂｉｔｒａｒｙＳｐａｔｉａｌＴｒｉａｎｇｕｌａｔｉｏｎＺｈｏｕＹｕｎｓｈｉ（周蕴时）；ＺｈａｎｇＸｕｅｍｅｉ（张雪梅）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，Ｕｎｉｖｅｒｓｉ...     

Papers of L.V. Kantorovich on bernstein polynomials

The issue of Bernstein polynomials is enough far from the basic range of Kantorovich’s interests. He devoted only two papers to them in 1930 and 1931 and made a report at the First All-Union Mathematical Congress in Khar’kov in 1930. However, these works contain two simple unique ideas, as well as their effective realization, in the theory of Bernstein polynomials. Both articles became the starting point for further research. Firstly, they gave a sample of the structures of polynomial approximants in terms of the Bernstein base. Secondly, they attracted attention to the problem of approximation by Bernstein polynomials in the complex domain of functions that are analytic at part of a segment [0, 1]. S.N. Bernstein took special interest in the second subject. He called Kantorovich’s article a wonderful work and published two brief notes in 1936 and a large paper in 1943 to develop the results.     

On the approximation of differentiable functions by Bernstein polynomials and Kantorovich polynomials

E.V. Voronovskaya and S.N. Bernstein established an asymptotic representation for the deviation of functions from Bernstein polynomials under the condition that the function has an even-order derivative. In the present paper, a similar problem is solved in the case when the function has an odd-order derivative. In addition, analogous representations are obtained for the deviations of functions from Kantorovich polynomials.     

第三型伯恩斯坦插值过程的双结点修正

In this work,the well-known problem put forward by S N Bernstein in 1930 is studied in a deep step.An operator is constructed by revising double interpolation nodes.It is proved that the operator converges to arbitrary continuous functions uniformly and the convergence order is the best.     

On a certain seqence of positive linear operators and tow optimization inequalities

In this Paper the approximation of continuous functions by positive linear operators of Bernstein type is investigated. The consideered operators are constructed using a system of rational functions with prescribed matrix of real poles. A certain general problem of S Bernstein concerning a scheme of construction of a sequence of positive linear operators is discussed. The answer on the Bernstein's hypothesis is given. The optimal limiting relations for the norm of the second central moment of our sequence of operators are established.     

Approximation by Müntz spaces on positive intervals

The so-called Bernstein operators were introduced by S.N. Bernstein in 1912 to give a constructive proof of Weierstrass? theorem. We show how to extend his result to Müntz spaces on positive intervals.     

Which perturbations of quasianalytic weights preserve quasianalyticity? How to use de Branges’ theorem

Based on an approach of de Branges and the theory of entire functions, we prove two results pertaining to the Bernstein approximation problem, one concerning analytic perturbations of quasianalytic weights and the other dealing with density of polynomials in spaces with nonsymmetric weights. We improve earlier results of V. P. Gurarii and A. Volberg, giving a more complete answer to a question posed by L. Ehrenpreis and S. N. Mergelyan.     

The complete asymptotic expansion for Bernstein operators

In this paper we study the asymptotic behavior of the classical Bernstein operators, applied to q-times continuously differentiable functions. Our main results extend the results of S.N. Bernstein and R.G. Mamedov for all q-odd natural numbers and thus generalize the theorem of E.V. Voronovskaja. The exact degree of approximation is also proved.     

Inclusion relations for Bernstein quasi-analytic classes

The inclusion relations for classes of quasi-analytic functions introduced by S. N. Bernstein are studied. A criterion for determining when such a class is a subset of another is established. This is accomplished with the aid of a counting function associated with the class.     

Inequalities for polynomials with restricted coefficients

We obtain other refinements of the inequalities of S. N. Bernstein and M. Riesz for polynomials. The methods of proof use the theory of boundpreserving convolution operators in the unit disk and interpolation formulas.     

ON A THEOREM OF BERNSTEIN AND ITS APPLICATIONS TO WEIGHTED MINIMAX SERIES

1.IntroductionLetfbeacontinuousfunctionon[a,b].L[.willdesignatethesetofallpolynomialsofdegreelessorequalthannand11thesetofallpolyflomials.Asiswellknown,foreachntheminimaxoffisgivenby:wherepnisthebestuniformapproximationoffin11..LetusalsoconsidertileminimaxseriesgivenbytheexpressionThesetoffunctionsforwhichS*(f)=ZEd(f)相似文献