共查询到20条相似文献,搜索用时 31 毫秒
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丁春梅 《数学物理学报(A辑)》2010,30(1):142-153
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. 相似文献
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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. 相似文献
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Li Cheng Linsen Xie 《分析论及其应用》2006,22(3):246-253
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. 相似文献
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Zhou D. X. 《Journal of Approximation Theory》1995,81(3)
We characterize the higher orders of smoothness of functions in C[0, 1] by Bernstein polynomials and Kantorovich operators. This task is carried out by means of the rate of convergence for combinations of these operators and the behavior of their derivatives. 相似文献
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Ding-Xuan Zhou 《Results in Mathematics》1995,28(1-2):169-183
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. 相似文献
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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. 相似文献
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Ioan Gavrea 《Journal of Computational Analysis and Applications》2001,3(3):249-257
We investigate the global smoothness preservation by Bernstein operators measured by second-order modulus of smoothness and give a partial answer for a conjecture raised by H. H. Gonska in 1998. 相似文献
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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. 相似文献
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关于Bernstein型多项式导数的特征 总被引:5,自引:1,他引:4
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。 相似文献
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Gancho Tachev 《Mathematica Slovaca》2013,63(5):1153-1161
We establish the global smoothness preservation of a function f by the sequence of linear positive operators. Our estimate is in terms of the second order Ditzian-Totik modulus of smoothness. Application is given to the Bernstein operator. 相似文献
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Linearkombinationen von iterierten Bernsteinoperatoren 总被引:1,自引:0,他引:1
Günter Felbecker 《manuscripta mathematica》1979,29(2-4):229-248
The Bernstein polynomials Bn(f) approximate every function f which is continuous on [0, 1] uniformly on [0, 1]. Also the derivatives of the Bernstein polynomials approach the derivatives of the function f uniformly on [0, 1], if f has continuous derivatives. In this paper we shall introduce polynomial operators, namely linear combinations of iterates of Bernstein operators, which have the same properties but, under definite conditions, approximate f more closely than the Bernstein operators. 相似文献
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We will use the method introduced in the first part of our paper (see [5]) to give the best lower estimate of ∥f - B n f ∥ for the Bernstein polynomial operators by means of a modified modulus of smoothness. The key role in our approach is the estimate of the derivative of the iterated Bernstein polynomial operators. 相似文献
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Our results describe how quantitative properties of univariate operators are inherited by the tensor product of their parametric extensions. This includes statements concerning simultaneous approximation. The estimates are in terms of partial and total moduli of smoothness of higher order. Applications are given for cubic interpolatory splines and Bernstein operators. Further applications are possible. 相似文献
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For the Bernsteinoperators M. Felten[]gave the direct inverseestimates by theDitzian-Totik modulus of smoothness ωφ 《数学进展》2000,29(2):174-175
For the Bernstein operators, M. Felten[1] gave the direct and inverseestimates by the Ditzian-Totik modulus of smoothness ω2(f,t), whereby the step-weight is a function as such that 相似文献
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We supplement recent results on a class of Bernstein–Durrmeyer operators preserving linear functions. This is done by discussing
two limiting cases and proving quantitative Voronovskaya-type assertions involving the first-order and second-order moduli
of smoothness. The results generalize and improve earlier statements for Bernstein and genuine Bernstein–Durrmeyer operators. 相似文献
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Ana‐Maria Acu Carmen Violeta Muraru Daniel Florin Sofonea Voichiţa Adriana Radu 《Mathematical Methods in the Applied Sciences》2016,39(18):5636-5650
In this paper, we will propose a Durrmeyer variant of q‐Bernstein–Schurer operators. A Bohman–Korovkin‐type approximation theorem of these operators is considered. The rate of convergence by using the first modulus of smoothness is computed. The statistical approximation of these operators is also studied. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Linsen Xie 《Archiv der Mathematik》2008,91(1):86-96
In this paper we study the saturation class for the linear combinations of Bernstein operators. The characterization of the
saturation class involving the modulus of smoothness is proved under certain assumption.
Received: 1 September 2007 相似文献
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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. 相似文献
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单纯形上加权K—泛函与光滑模的等价性及其应用 总被引:1,自引:1,他引:0
本文首先讨论了高维单纯形上一类加权K-泛函与光滑模的等价性。然后作为应用,给出了高维单纯形上多元Bernstein算子加权逼近的特征刻划。 相似文献