修正的q-Baskakov-Durrmeyer-Stancu算子的逼近性质

基于q-微积分的概念引入一类修正的Stancu型q-Baskakov-Durrmeyerr算子,并且借助连续模研究该算子的一些局部逼近性质,得到了算子的局部逼近定理.同时讨论的算子的加权逼近.     

Bernstein型算子加Jacobi权逼近

对于Bernstein型算子,证明它在通常的加权范数下是无界的,通过引进新的加权范数,研究其加Jacobi权的逼近性质,得到加权逼近的正逆定理,从而导出加权逼近特征的等价刻画．     

某些多元线性正算子的加权逼近

本文首先给出了在Ｌｐ逼近意义下某些线性正算子加Ｊａｃｏｂｉ权逼近时的特征定理，作为应用，我们给出了多元Ｂａｓｋａｋｏｖ型算子、多元Ｓｚａｓｚ－Ｍｉｒａｋｊａｎ型算子和多元Ｂｅｔａ算子加权逼近时的特征刻划．     

一类多元Gauss-Weierstrass 算子线性组合的加权Lp-逼近

本文研究一类多元Gauss-Weierstrass算子的线性组合加Jacobi型权逼近的性质,利用加权矩量不等式及加权K-泛函、光滑模等工具,建立了这类算子在Lp(1≤p≤∞)空间的正、逆定理和逼近阶的特征刻划.     

LBRAGIMOV-GADJIEV-DURRMEYER算子在ORLICZ空间内的逼近性质

本文研究了lbragimov-Gadjiev-Durrmeyer算子在Orlicz空间内的逼近问题.借助了Jensen不等式,H?lder不等式,K泛函,光滑模等工具,获得了lbragimov-Gadjiev-Durrmeyer算子在Orlicz空间内的逼近度,以及该算子的加权逼近,推广了lbragimov-Gadjiev-Durrmeyer算子在L_p空间中的逼近度及加权逼近.     

关于混合指数型积分算子的加权逼近

1987年,Z.Ditzian和V.Totik在[1]中研究了指数型算子的加权逼近问题,1989年,陈文忠教授在[2]中研究了混合指数型积分算子在C-空间的逼近性质,本文则是研究一类混合指数型积分算子在L_p空间的加权逼近问题。     

关于Baskakov型算子的加权逼近

本文首先研究在通常的加权范数下,给出了Baskakov-Durrmeyer算子加Jacobi权逼近时的特征刻划;然后指出在通常的加权范数下,Baskakov算子在加Jacobi权逼近时是无界的.通过引入一种新的加权范数和新的k-泛函,给出了加权逼近时的特征定理。     

Szász-Mirakjan算子逐点加权同时逼近

本文研究了Szász-Mirakjan算子加权同时逼近的问题.利用加权光滑模ω2φλ(f,t)u,获得了Szász-Mirakjan算子加权同时逼近的点态结果,推广了已知的结果.     

Szsz-Mirakjan算子逐点加权同时逼近(英文)

本文研究了Szsz-Mirakjan算子加权同时逼近的问题.利用加权光滑模ω2φλ(f,t)ω,获得了Szsz-Mirakjan算子加权同时逼近的点态结果,推广了已知的结果.     

修正的Picard算子在Orlicz空间中的指数加权逼近

本文研究修正的Picard算子在Orlicz空间内指数加权逼近的收敛性和逼近性质.通过建立Orlicz空间内指数加权逼近的相关引理,利用H?lder不等式,Korovkin定理,凸函数的Jensen不等式, Minkowski不等式及相关分析技巧得出该算子在Orlicz空间中指数加权逼近的正定理及相关性质.     

Baskakov算子线性组合加Jacobi权逼近及高阶导数的正逆定理

利用加权光滑模ωrψλ(f,t)ω给出了Baskakov算子的线性组合加Jacobi权逼近的正逆定理;另外,研究了加Jacobi权下Baskakov算子的高阶导数与所逼近函数光滑性之间的关系.     

Equivalent theorems on simultaneous approximation by combinations of Gamma operators

In this paper,some equivalent theorems on simultaneous approximation for combinations of Gamma operators by weighted moduli of smoothness ωr(4)λ(f,t)w(4)s(O≤λ≤1)are given.The relation between derivatives of combinations of Gamma operators and smoothness of derivatives of functions is also investigated.     

Stancu-Sikkema算子的点态估计

本文构造了Stancu—Sikkema算子,并利用点态光滑模研究了此算子的点态逼近正逆定理.     

Strong type of Steckin inequality for the linear combination of Bernstein operators

In this paper we obtain a new strong type of Steckin inequality for the linear combinations of Bernstein operators, which gives the optimal approximation rate. Moreover, a method to prove lower estimates for linear operators is introduced. As a result the lower estimate for the linear combinations of Bernstein operators is obtained by using the Ditzian–Totik modulus of smoothness.     

APPROXIMATION BY A CLASS OF MODIFIED SZASZ-DURRMEYER OPERATORS

ThisprojectissupportedbyZhejiangProvincialFoundationofChina.1.IntroductionForjEC[0,1]ther-thBernsteinpolynomialisdefinedbyItwasshownbyH.BerensandG.G.Lorentz([2]in1972)thatif0相似文献   

On a Problem of Gonska

This paper investigates global smoothness preservation by the Bernstein operators. When the smoothness is measured by the modulus of continuity, this problem is well understood. When it is measured by the second order modulus of smoothness, H. Gonska conjectured that the Lipschitz classes of second order keep invariate under the Bernstein operators. Here we present a counterexample to this conjecture. Then we introduce a new modulus of smoothness and show that the Lip-α(0 < α ≤ 1) classes measured by this modulus are invariate under the Bernstein operators. By means of this modulus we also improve some previous results concerning global smoothness preservation.     

On the characterization of the smoothness of skew-adjoint potentials in periodic Dirac operators

In this paper we consider periodic Dirac operators with skew-adjoint potentials in a large class of weighted Sobolev spaces. We characterize the smoothness of such potentials by asymptotic properties of the periodic spectrum of the corresponding Dirac operators.     

Szász-Mirakjan算子线性组合和导数的点态逼近定理

本文给出了Szász-Mirakjan算子线性组合的点态逼近定理。另外,还研究了Szász-Mirakjan算子高阶导数与所逼近函数光滑性之间的关系。     

Smoothness Properties of Modified Bernstein-Kantorovich Operators

In this article, we consider modified Bernstein-Kantorovich operators and investigate their approximation properties. We show that the order of approximation to a function by these operators is at least as good as that of ones classically used. We obtain a simultaneous approximation result for our operators. Also, we prove two direct approximation results via the usual second-order modulus of smoothness and the second-order Ditzian-Totik modulus of smoothness, respectively. Finally, some graphical illustrations are provided.     

Properties of a Family of Operators

In this paper we define a family of new nonsymmetric operators of generalized translation and describe their properties. For each of these operators, we introduce a generalized modulus of smoothness, for which the direct and inverse theorems of approximation theory are given.