多元Bernstein算子的导数与函数的光滑性

利用一个新的光滑性度量刻画多元Bernstein算子方向导数的特征,建立Bernstein算子的导数与逼近函数光滑性之间的等价关系。同时,一个关于一元Bernstein算子的相应结果被推广到多元情形。     

Bernstein型算子线性组合加Jacobi权逼近及高阶导数的等价定理

本文利用加权Ditzian-Totik光滑模证明Bernstein型算子的线性组合加权逼近阶估计和等价定理;同时,研究加Jacobi权下Benstein型算子的高阶导数与所逼近函数光滑性之间的关系.     

关于Bernstein型多项式导数的特征

利用高阶光滑模研究Bernstein型多项式的高阶导数问题，用函数的光滑性刻画Bernstein型多项式的高阶导数的特征，得到了一个等价定理。     

Bernstein 算子的同时逼近

借助于D itzian-T otik光滑模研究了Bernstein算子的同时逼近问题,给出了Bernstein算子同时逼近的正定理和等价定理.     

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     

Bernstein算子的点态同时逼近

借助光滑模ω_φ~2(f,t)(φ是一般步权函数),研究了Bernstein算子的点态同时逼近问题,给出了Bernstein算子同时逼近的等价定理,建立了其导数与光滑函数间的关系,对以前已有的结果予以补充和完善.     

Bernstein算子线性组合同时逼近的点态估计

借助于光滑模ωψ^rλ（f,t）（0≤λ≤1）给出了Bernstein算子线性组合同时逼近的点态结果。     

关于Bernstein算子的收敛速度

本文对一类函数建立了Bernstein算子的一致逼近定理,而且给出了其逆定理的一个简短证明。     

左Bernstein逆插值算子的点态逼近性质

利用光滑模ω2φrλ(f,t)给出了左Bernste in逆插值算子的逼近等价定理.     

Bernstein型算子同时逼近误差

该文证明了C[0,1]空间中的函数及其导数可以用Bernstein算子的线性组合同时逼近,得到逼近的正定理与逆定理.同时,也证明了Bernstein算子导数与函数光滑性之间的一个等价关系.该文所获结果沟通了Bernstein算子同时逼近的整体结果与经典的点态结果之间的关系.     

Derivatives of multidimensional Bernstein operators and smoothness

We characterize the directional derivatives of multidimensional Bernstein operators by a new measure of smoothness. This task is carried out by means of establishing the relation between the asymptotic behavior of the derivatives and the smoothness of the functions they approximate. The obtained results generalize the corresponding ones for univariate Bernstein operators.     

Pointwise weighted approximation by Bernstein operators

We consider the pointwise weighted approximation by Bernstein operators. The related weight functions are Jacobi weights . We obtain approximation equivalence theorems, using a weighted modulus of smoothness , which is an extension of~[5].     

Global smoothness preservation by bivariate interpolation operators

1　IntroductionIn the case when Pn(f,x) represents the univariate interpolation polynomial of Her-mite-Fejér based on Chebyshev nodesof the firstkind or the univariate interpolation polyno-mials of Lagrange based on Chebyshev nodes of the second kind and± 1 ,or the univariaterational Shepard operators,the following result of partial preservation of global smoothnessis proved in[4] :If f∈Lip M(α;[-1 ,1 ] ) ,0 <α≤ 1 ,then there existsβ=β(α) <α and M′>such thatω(Pn(f ) ;h)≤ M′h…     

Pointwise Approximation Theorems for Combinations and Derivatives of Bernstein Polynomials

We establish the pointwise approximation theorems for the combinations of Bernstein polynomials by the rth Ditzian-Totik modulus of smoothness wФ^r（f, t） where Ф is an admissible step-weight function. An equivalence relation between the derivatives of these polynomials and the smoothness of functions is also obtained.     

On an extremal relation of Bernstein operators

In this note we present a new characterization of Bernstein operators by showing that they are the only solution of a certain extremal relation.     

Equivalent theorems on simultaneous approximation by combinations of Bernstein operatores

In this paper we give equivalent theorems on simultaneous approximation for the combinations of Bernstein operators by r-th Ditzian-Totik modulus of smoothness ωτψλ (f, t)(0 ≤λ≤ 1). We also investigate the relation between the derivatives of the combinations of Bernstein operators and the smoothness of derivatives of functions.