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Weighted approximation of functions with singularities by Bernstein operators 被引量:8
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作者 Bao-rong WEI Yi ZHAO 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2008年第10期1451-1456,共6页
As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimat... As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimates for weighted approximation of functions with singularities by Bernstein operators. The main results are the Jackson's estimates of functions f∈ (Wwλ)2 andre Cw, which extends the result of (Della Vecchia et al., 2004). 展开更多
关键词 Bemstein operators Functions with singularities weighted approximation Pointwise estimates
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Weighted Approximation by Left Quasi-interpolants of Derivatives of Gamma Operators
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作者 JIANG HONG-BIAO 《Communications in Mathematical Research》 CSCD 2009年第4期289-298,共10页
In order to obtain much faster convergence, Miiller introduced the left Gamma quasi- interpolants and obtained an approximation equivalence theorem in terms of 2r wφ (f,t)p. Cuo extended the MiiUer's results to w... In order to obtain much faster convergence, Miiller introduced the left Gamma quasi- interpolants and obtained an approximation equivalence theorem in terms of 2r wφ (f,t)p. Cuo extended the MiiUer's results to wφ^24 (f, t)∞. In this paper we improve the previous results and give a weighted approximation equivalence theorem. 展开更多
关键词 Gamma operator quasi-interpolant weighted approximation modulus of smoothness derivative
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WEIGHTED APPROXIMATION OF RANDOM FUNCTIONS
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作者 YU JIARONG 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1995年第4期361-366,共6页
Let (Ω, A, P) be a probability space, X(t, ω) a random function continuous in probability for t∈[0,+∞) or (-∞,+∞)(ω∈Ω), and F(t) a positive function continuous for t∈[0,+∞) or (-∞, +∞). If X(t, ω) and F(... Let (Ω, A, P) be a probability space, X(t, ω) a random function continuous in probability for t∈[0,+∞) or (-∞,+∞)(ω∈Ω), and F(t) a positive function continuous for t∈[0,+∞) or (-∞, +∞). If X(t, ω) and F(t) verify certain conditions, then there exists a sequence {Qn(t,ω)} of random polynomials such that we have almost surely: for t∈[0,+∞) or (-∞, +∞), lim|X(t, ω)-Qn(t, ω)|/F(t)=0. 展开更多
关键词 Random function continuous in probability weighted approximation.
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On Weighted Approximation by Modified Bernstein Operators for Functions with Singularities
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作者 Meiling Wang Dansheng Yu 《Analysis in Theory and Applications》 2014年第4期405-416,共12页
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 pointwi... 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. 展开更多
关键词 Modified Bernstein operators weighted approximation Stechkin inequality.
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WEIGHTED APPROXIMATION ON SZASZ-TYPE OPERATORS
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作者 Feng Guo (Taizhou University, China) 《Analysis in Theory and Applications》 2003年第1期47-54,共8页
In this paper, we use weighted modules ω(?)(f,t)w to study the pointwise approximation on Szasz-type operators, and obtain the direct and converse theorem, as well as characterizations of the pointwise approximation ... In this paper, we use weighted modules ω(?)(f,t)w to study the pointwise approximation on Szasz-type operators, and obtain the direct and converse theorem, as well as characterizations of the pointwise approximation of Jacobi-weighted Szasz-type operators. 展开更多
关键词 Szasz-type operator weighted modulus weighted approximation character itation
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Weighted Approximation of Kantorovich-Type Operator of Butzer-Hahn
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作者 田军 王绍钦 王玉 《Journal of Southwest Jiaotong University(English Edition)》 2005年第1期95-102,共8页
A kind of Kantorovich-type operator of Butzer-Hahn B*_n(f; x) on the bounded and integrable function space was introduced, and the properties of B*_n(f; x) were studied. Positive theorem, converse theorem, and the ord... A kind of Kantorovich-type operator of Butzer-Hahn B*_n(f; x) on the bounded and integrable function space was introduced, and the properties of B*_n(f; x) were studied. Positive theorem, converse theorem, and the order of weighted ~approximation of B*_n(f; x) were obtained. 展开更多
关键词 Kantorovich-type operator of Butzer-Hahn Properties of approximation weighted approximation
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Approximation by the Modified q-Baskakov-Szsz Operators 被引量:1
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作者 Qingfeng Mo Xiaomin Hu 《Analysis in Theory and Applications》 2014年第3期281-289,共9页
In this paper we propose the q analogues of modified Baskakov-Sz^sz op- erators. We estimate the moments and established direct results in term of modulus of continuity. An estimate for the rate of convergence and wei... In this paper we propose the q analogues of modified Baskakov-Sz^sz op- erators. We estimate the moments and established direct results in term of modulus of continuity. An estimate for the rate of convergence and weighted approximation properties of the q operators are also obtained. 展开更多
关键词 q-analogues Baskakov-Szasz operator modulus of continuity weighted approximation
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Convergence of the q Analogue of Szász-Beta-Stancu Operators
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作者 Yang Xu Xiaomin Hu 《Analysis in Theory and Applications》 CSCD 2015年第1期45-57,共13页
In the present paper, we propose the q analogue of Szasz-Beta-Stancu operators. By estimate the moments, we establish direct results in terms of the modulus of smoothness. Investigate the rate of point-wise convergenc... In the present paper, we propose the q analogue of Szasz-Beta-Stancu operators. By estimate the moments, we establish direct results in terms of the modulus of smoothness. Investigate the rate of point-wise convergence and weighted approximation properties of the q operators. Voronovskaja type theorem is also obtained. Our results generalize and supplement some convergence results of the q-Szasz-Beta operators, thus they improve the existing results. 展开更多
关键词 q-Szasz-Beta operators q-analogues modulus of smoothness stancu weighted approximation.
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Some Approximation Properties of Certain q-Baskakov-Beta Operators
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作者 Ruirui Liu Xiaomin Hu Huating Wu 《Analysis in Theory and Applications》 CSCD 2016年第2期189-204,共16页
In this paper, we propose the q analogue of modified Baskakov-Beta operators. The Voronovskaja type theorem and some direct results for the above operators are discussed. The rate of convergence and weighted approxima... In this paper, we propose the q analogue of modified Baskakov-Beta operators. The Voronovskaja type theorem and some direct results for the above operators are discussed. The rate of convergence and weighted approximation by the operators are studied. 展开更多
关键词 q-Baskakov-Beta operators rate of convergence weighted approximation.
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Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid
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作者 ZHOUShi-Qi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2002年第5期543-548,共6页
A systematic methodology is proposed to deal with the weighted density approximation version of clas-sical density functional theory by employing the knowledge of radial distribution function of bulk fluid. The presen... A systematic methodology is proposed to deal with the weighted density approximation version of clas-sical density functional theory by employing the knowledge of radial distribution function of bulk fluid. The presentmethodology results from the concept of universality of the free energy density functional combined with the test particlemethod. It is shown that the new method is very accurate for the predictions of density distribution ofa hard sphere fluidat different confining geometries. The physical foundation of the present methodology is also applied to the quantumdensity functional theory. 展开更多
关键词 density functional theory weighted density approximation radial distribution function
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Approximation by the q-Baskakov-Schurer-Szász-Beta Operators
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作者 吴华亭 胡晓敏 刘蕊蕊 《Chinese Quarterly Journal of Mathematics》 2016年第3期269-278,共10页
In this paper we introduce a new kind of Baskakov-Schurer-Szasz-Beta operators M^qn,p based on q-integers. We establish some direct results in the polynomial weighted space of continuous functions defined on the inter... In this paper we introduce a new kind of Baskakov-Schurer-Szasz-Beta operators M^qn,p based on q-integers. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, ∞]. Then we obtain the estimates on the rate of convergence and weighted approximation of operators M^qn,p in terms of modulus of continuity. 展开更多
关键词 q-Baskakov-Schurer-szdsz-Beta operators rate of convergence q-analogues modulus of continuity weighted approximation
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Some Approximation Properties of Certain q-Sz′asz-Mirakyan-Baskakov Operators
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作者 莫庆峰 胡晓敏 吴鹏 《Chinese Quarterly Journal of Mathematics》 2015年第4期587-595,共9页
In this paper we propose the q analogues of modified Baskakov-Szasz operators. we estimate the moments and establish the direct results in term of modulus of continuity. An estimate for the rate of convergence and wei... In this paper we propose the q analogues of modified Baskakov-Szasz operators. we estimate the moments and establish the direct results in term of modulus of continuity. An estimate for the rate of convergence and weighted approximation properties of the q operators axe also obtained. 展开更多
关键词 q-Sz′asz-Mirakyan-Baskakov operators q-analogues modulus of continuity weighted approximation
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Weighted Approximation by Multidimensional Baskakov Operators 被引量:1
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作者 游功强 宣培才 《Journal of Mathematical Research and Exposition》 CSCD 2000年第1期43-50,共8页
In this paper, we shall point out that the Multidimensional Baskakov opera- tors are unbounded in . Then we give a inverse theorems for multivariate Baskakov operators with Jacobi weights. A crucial tools in our app... In this paper, we shall point out that the Multidimensional Baskakov opera- tors are unbounded in . Then we give a inverse theorems for multivariate Baskakov operators with Jacobi weights. A crucial tools in our approach is a decompo- sition technique and a new type weights norm and flew K-function 展开更多
关键词 Multivariate Baskakov operators: Jacobi weights weighted approximation claracterization.
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Weighted approximation by Bernstein quasiinterpolants for functions with singularities 被引量:2
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作者 Yi ZHAO Dansheng YU 《Frontiers of Mathematics in China》 SCIE CSCD 2013年第6期1461-1479,共19页
We introduce a new type of modified Bernstein quasi-interpolants, which can be used to approximate functions with singularities. We establish direct, inverse, and equivalent theorems of the weighted approximation of t... We introduce a new type of modified Bernstein quasi-interpolants, which can be used to approximate functions with singularities. We establish direct, inverse, and equivalent theorems of the weighted approximation of this modified quasi-interpolants. Some classical results on approximation of continuous functions are generalized to the weighted approximation of functions with singularities. 展开更多
关键词 Quasi-interpolants function with singularities Bernstein operator weighted approximation equivalent theorem
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K-Functional, Weighted Moduli of Smoothness, and Best Weighted Polynomial Approximation on a Simplex
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作者 Song Li Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1999年第3期395-403,405-406,共11页
An inverse theorem for the best weighted polynomial approximation of a function in L<sub>w<sub>α</sub></sub><sup>p</sup>(S) is established. We also investigate Besov spaces gener... An inverse theorem for the best weighted polynomial approximation of a function in L<sub>w<sub>α</sub></sub><sup>p</sup>(S) is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial approximation in L<sub>p</sub>(R)w<sub>λ</sub>, where w<sub>α</sub> is a Jacobi-type weight on S, 0【p≤∞, S is a simplex and W<sub>λ</sub> is a Freud weight. For Ditzian-Totik K-functionals on L<sub>P</sub>(S), 1≤P≤∞, we obtain a new equivalence expression. 展开更多
关键词 weighted moduli of smoothness K-FUNCTIONAL Best weighted polynomial approximation SIMPLEX
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Approximation by q Baskakov Beta Operators 被引量:2
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作者 Vijay GUPTA Ali ARAL 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2011年第4期569-580,共12页
In the present paper we introduce the q analogue of the Baskakov Beta operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, ∞). Then we obta... In the present paper we introduce the q analogue of the Baskakov Beta operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, ∞). Then we obtain point-wise estimate, using the Lipschitz type maximal function. 展开更多
关键词 q-Baskakov operators q-Baskakov-Beta operators modulus of continuity K-FUNCTIONAL weighted approximation rate of approximation q-Beta integral
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Bootstrap Approximation to the Distribution of M-estimates in a Linear Model 被引量:1
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作者 XiaoMingWANG WangZHOU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2004年第1期93-104,共12页
The authors establish the approximations to the distribution of M-estimates in a linear model by the bootstrap and the linear representation of bootstrap M-estimation, and prove that the approximation is valid in prob... The authors establish the approximations to the distribution of M-estimates in a linear model by the bootstrap and the linear representation of bootstrap M-estimation, and prove that the approximation is valid in probability 1. A simulation is made to show the effects of bootstrap approximation, randomly weighted approximation and normal approximation. 展开更多
关键词 Linear model M-estimate Linear representation Bootstrap approximation Normal approximation Randomly weighted approximation
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SPECTRAL METHOD FOR MIXED INHOMOGENEOUS BOUNDARY VALUE PROBLEMS IN THREE DIMENSIONS 被引量:1
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作者 Tianjun Wang Benyu Guo Wei Li 《Journal of Computational Mathematics》 SCIE CSCD 2012年第6期579-600,共22页
In this paper, we investigate spectral method for mixed inhomogeneous boundary value problems in three dimensions. Some results on the three-dimensional Legendre approxima- tion in Jacobi weighted Sobolev space are es... In this paper, we investigate spectral method for mixed inhomogeneous boundary value problems in three dimensions. Some results on the three-dimensional Legendre approxima- tion in Jacobi weighted Sobolev space are established, which improve and generalize the existing results, and play an important role in numerical solutions of partial differential equations. We also develop a lifting technique, with which we could handle mixed inho- mogeneous boundary conditions easily. As examples of applications, spectral schemes are provided for three model problems with mixed inhomogeneous boundary conditions. The spectral accuracy in space of proposed algorithms is proved. Efficient implementations are presented. Numerical results demonstrate their high accuracy, and confirm the theoretical analysis well. 展开更多
关键词 Three-dimensional Legendre approximation in Jacobi weighted Sobolev space Lifting technique Spectral method for mixed inhomogeneous boundary value problems.
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