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1.
We obtain the complete asymptotic expansion of the image functions of Müller’s Gamma operators and of their derivatives. All expansion coefficients are explicitly calculated. Moreover, we study linear combinations of Gamma operators having a better degree of approximation than the operators themselves. Using divided differences we define general classes of linear combinations of which special cases were recently introduced and investigated by other authors. 相似文献
2.
Lin Sen XIE Zhong Rui SHI 《数学学报(英文版)》2007,23(5):935-944
In this paper, we investigate the relation between the rate of convergence for the derivatives of the combinations of Baskakov operators and the smoothness for the derivatives of the functions approximated. We give some direct and inverse results on pointwise simultaneous approximation by the combinations of Baskakov operators. We also give a new equivalent result on pointwise approximation by these operators. 相似文献
3.
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
4.
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
5.
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. 相似文献
6.
Li Bingzheng 《分析论及其应用》1993,9(3):61-72
We consider the linear combinations of Baskakov-Durrmeyer operators and give the characterization in terms of the classical
modulous of smoothness for ∞-norm by the means of the pointwise simultanrous approximation. An equivalence ralation between
the derivatives of these operators and smoothness of functions is also presented.
Supported by Zhejiang Provincial Foundation of China. 相似文献
7.
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。 相似文献
8.
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
9.
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
10.
11.
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
12.
The aim of the paper is to characterize the global rate of approximation of derivativesf(l)through corresponding derivatives of linear combinations of Post–Widder operators in an appropriate weightedLp-metric using a weighted Ditzian and Totik modulus of smoothness, and also to characterize derivatives of these operators in Besov spaces of Ditzian–Totik type. 相似文献
13.
Feilong Cao 《Journal of Approximation Theory》2005,132(2):241-257
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. 相似文献
14.
15.
In this paper,we obtain the strong converse inequality for Szász operators with K-functional by introducing a new K-functional of the form Kαλ(f,t2) = infg∈C2λ{‖f-g‖0 t2‖g‖2}(0≤λ≤1,0<α<2),where ‖·‖0,‖·‖2,C2λ are defined in the paper.As for its applications,we have extended some results before this paper. 相似文献
16.
Guangshi Lü 《Monatshefte für Mathematik》2013,169(3-4):409-422
Let S k (Γ) be the space of holomorphic cusp forms of even integral weight k for the full modular group. Let λ f (n), λ g (n), λ h (n) be the nth normalized Fourier coefficients of three distinct holomorphic primitive cusp forms ${f (z) \in S_{k_1}(\Gamma), g(z) \in S_{k_2} (\Gamma), h(z) \in S_{k_3} (\Gamma)}$ respectively. In this paper we are able to establish nontrivial estimates for $$\sum_{n{\leq}x} \lambda_f(n)^5{\lambda_g}(n), \quad \sum_{n{\leq}x} \lambda_f(n) \lambda_g(n)\lambda_{h}(n)^j$$ , where 1 ≤ j ≤ 4. 相似文献
17.
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
18.
Vesselin Vatchev 《分析论及其应用》2011,27(2):187-200
For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln(ψ) = n ∑ k=0 akψ(k), where the constant coefficients ak ∈ R may be adapted to f . We prove that for each f ∈ C(n)(I), there is a selection of coefficients {a1, ,an} and a corresponding linear combination Sn( f ,t) = n ∑ k=1 bkeλkt of functions ψk(t) = eλkt in the nullity of L which satisfies the following Jackson’s type inequality: f (m) Sn(m )( f ,t) ∞≤ |an|2n|Im|1/1q/ep|λ|λn|n|I||nm1 Ln( f ) p, where |λn| = mka x|λk|, 0 ≤ m ≤ n 1, p,q ≥ 1, and 1p + q1 = 1. For the particular operator Mn(f) = f + 1/(2n) f(2n) the rate of approximation by the eigenvalues of Mn for non-periodic analytic functions on intervals of restricted length is established to be exponential. Applications in algorithms and numerical examples are discussed. 相似文献
19.
Shunsheng GuoLixia Liu Qiulan Qi 《Journal of Mathematical Analysis and Applications》2002,265(1):135-147
For linear combinations of Bernstein-Kantorovich operators Kn, r(f, x), we give an equivalent theorem with ω2r?λ(f, t). The theorem unites the corresponding results of classical and Ditzian-Totik moduli of smoothness. 相似文献
20.
本文首先给出了Baskakov-Durrmeyer算子在一致副近意义下的正定理,并把它推广到一类线性组合的情形,然后讨论了它的导数与光滑模的等价关系,最后给出了二元Baskakov-Durrmeyer算子逼近阶的特征刻画. 相似文献