共查询到18条相似文献,搜索用时 46 毫秒
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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对逼近的特征刻划定理. 相似文献
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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
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Bernstein型多项式逼近的逆定理 总被引:1,自引:0,他引:1
对于Bernstein型多项式,利用强Voronovskaja型展开,证明该多项式逼近连续函数强型逆定理,从而用Ditzian-Totik模刻画该多项式逼近阶的特征,得到了等价刻画定理. 相似文献
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了一个典型的non-caratheodory区域上的多项加权一致逼近结果,证明方法本身也给出了逼近的具体过程。 相似文献
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一类Bernstein型算子加权逼近 总被引:2,自引:1,他引:2
本文首先给出了一类用递归法定义的Bernsein型算子在一致逼近意义下的特征刻划,然后指出在通常的加权范数下,它虹无界的,通过引入的一种新范数,我们给出了该算子加Jacobi权逼近的特征刻划。 相似文献
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关于多元Baskakov算子的加权逼近 总被引:1,自引:0,他引:1
本文首先指出一类多元Baskakov算子在通常的加权范数下是无界的.然后给出了一类新的加权范数,在此范数下它是压缩的.最后利用多元分解技巧,解决了多元Baskakov算子加权逼近的特征刻划文问题. 相似文献
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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
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
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研究Bernstein-Durrmeyer多项式的加权逼近并建立其饱和定理. 相似文献
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Pointwise Approximation Theorems for Combinations
and Derivatives of Bernstein Polynomials 总被引:1,自引:0,他引:1
Lin Sen XIE 《数学学报(英文版)》2005,21(5):1241-1248
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. 相似文献
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We introduce a new type of Bernstein polynomials, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type of combinations are obtained. 相似文献
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In this paper, the multivariate Bernstein polynomials defined on a simplex are viewed as sampling operators, and a generalization by allowing the sampling operators to take place at scattered sites is studied. Both stochastic and deterministic aspects are applied in the study. On the stochastic aspect, a Chebyshev type estimate for the sampling operators is established. On the deterministic aspect, combining the theory of uniform distribution and the discrepancy method, the rate of approximating continuous function and L p convergence for these operators are studied, respectively. 相似文献
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Della Vecchia et al. (see [2]) introduced a kind of modified Bernstein operators which can be used to approximate functions with singularities at endpoints on [0,1]. In the present paper, we obtain a kind of pointwise Stechkin-type inequalities for weighted approximation by the modified Bemsetin operators. 相似文献
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M. Felten 《Constructive Approximation》1998,14(3):459-468
Direct estimates for the Bernstein operator are presented by the Ditzian—Totik modulus of smoothness , whereby the step-weight φ is a function such that φ
2
is concave. The inverse direction will be established for those step-weights φ for which φ
2
and , are concave functions. This combines the classical estimate (φ=1 ) and the estimate developed by Ditzian and Totik ( ). In particular, the cases , λ∈[0,1] , are included.
August 2, 1996. Date revised: March 28, 1997. 相似文献
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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 相似文献
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This paper is devoted to study direct and converse approximation theorems of the generalized Bernstein operators Cn( f,sn,x) via so-called unified modulus ω2φλ( f,t), 0 ≤λ≤1. We obtain main results as follows ω2φλ( f,t) =O(tα)|Cn( f,sn,x)- f(x)| =O(n-12 δ1-λn(x))α,where δ2n(x) =max{φ2(x),1/n} and 0 α 2. 相似文献
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Lorenzo DAmbrosio 《Journal of Approximation Theory》2006,140(2):191-202
The purpose of this paper is to study some new concrete approximation processes for continuous vector-valued mappings defined on the infinite dimensional cube or on a subset of a real Hilbert space. In both cases these operators are modelled on classical Bernstein polynomials and represent a possible extension to an infinite dimensional setting.The same idea is generalized to obtain from a given approximation process for function defined on a real interval a new approximation process for vector-valued mappings defined on subsets of a real Hilbert space. 相似文献