We study certain weighted Bergman and weighted Besov spaces of holomorphic functions in the polydisk and in the unit ball.We seek conditions on the weight functions to guarantee that the dilations of a given function ...We study certain weighted Bergman and weighted Besov spaces of holomorphic functions in the polydisk and in the unit ball.We seek conditions on the weight functions to guarantee that the dilations of a given function converge to the same function in norm;in particular,we seek conditions on the weights to ensure that the analytic polynomials are dense in the space.展开更多
In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and...In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and G(z)=∑^(N)_(i)=1 A_(−i)z^(i),A_(i)ae culants.展开更多
The accessibility of urban public transit directly influences residents’quality of life,travel behavior,and social equity.Its correlation with housing prices has garnered significant attention across disciplines such...The accessibility of urban public transit directly influences residents’quality of life,travel behavior,and social equity.Its correlation with housing prices has garnered significant attention across disciplines such as geography,economics,and urban planning.Although much existing research focuses on the impact of individual transportation facilities on housing prices,there is a notable gap in comprehensive analyses that assess the influence of overall urban transit accessibility on housing market dynamics.This study selected the main urban area of Hefei,China,as a case to investigate the spatial distribution of housing prices and evaluate public transit accessibility in 2022.Employing techniques such as the optimized parameter geographical detector and local spatial regression models,the study aimed to elucidate the effects and underlying mechanisms of urban transit accessibility on housing prices.The findings revealed that:1)housing prices in Hefei exhibited a clustered spatial pattern,with high prices concentrated in the city center and lower prices in peripheral areas,forming three distinct high-price hotspots with a‘belt-like’distribution;2)public transit accessibility showed a‘coreperiphery’structure,with accessibility declining in a‘circumferential’pattern around the city center.Based on the‘housing price-accessibility’dimension,four categories were identified:high price-high accessibility(37.25%),high price-low accessibility(19.07%),low price-high accessibility(21.95%),and low price-low accessibility(21.73%);3)the impact of transit accessibility on housing prices was spatially heterogeneous,with bus travel showing the strongest explanatory power(0.692),followed by automobile,subway,and bicycle travel.The interaction of these transportation modes generated a synergistic effect on housing price differentiation,with most influencing factors contributing more than 25%.These findings offer valuable insights for optimizing the spatial distribution of public transit infrastructure and improving both urban housing quality and residents’living standards.展开更多
The paper gives a new way of constructing Hermite Fejer and Hermite interpolatory polynomials with the nodes of the roots of first kind of Chebyshev polynomials and gives the approximation order of these two kinds of...The paper gives a new way of constructing Hermite Fejer and Hermite interpolatory polynomials with the nodes of the roots of first kind of Chebyshev polynomials and gives the approximation order of these two kinds of operators. The approximation orders are described with the best rate of approximation of f by polynomials of degree N=(q+1)n 1 in L p w spaces.展开更多
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
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
In this paper we establish a result about uniformly equivalent norms and the convergence of best approximant pairs on the unitary ball for a family of weighted Luxemburg norms with normalized weight functions dependin...In this paper we establish a result about uniformly equivalent norms and the convergence of best approximant pairs on the unitary ball for a family of weighted Luxemburg norms with normalized weight functions depending on ε, when ε→ 0. It is introduced a general concept of Pade approximant and we study its relation with the best local quasi-rational approximant. We characterize the limit of the error for polynomial approximation. We also obtain a new condition over a weight function in order to obtain inequalities in Lp norm, which play an important role in problems of weighted best local Lp approximation in several variables.展开更多
In the present paper, we establish direct and converse theorems for weight-ed Bernstein-Durrmeyer operators under weighted L^p-norm with Jacobi weight w（x）=x^a（1-x）β.All the results involved have no restriction a...In the present paper, we establish direct and converse theorems for weight-ed Bernstein-Durrmeyer operators under weighted L^p-norm with Jacobi weight w（x）=x^a（1-x）β.All the results involved have no restriction a,β〈1-1/p,which indicates that the weighted Bemstein-Durrmeyer operators have some better approxi- mation properties than the usual Bernstein-Durrmeyer operators.展开更多
We prove some approximation properties of generalized Meyer-Konig and Zeller operators for differentiable functions in polynomial weighted spaces. The results extend some results proved in [1-3,7-16].
The author consides Beta operators βnf on suitable Sobolev type subspace of Lp[0, ∞) and characterizes the global rate of approximation of derivatives f(r) through corresponding derivatives (βnf)(r) in an appropria...The author consides Beta operators βnf on suitable Sobolev type subspace of Lp[0, ∞) and characterizes the global rate of approximation of derivatives f(r) through corresponding derivatives (βnf)(r) in an appropriate weighted Lp-metric by the rate of Ditzian and Totik's r-th order weighted modulus of Smoothness.展开更多
We generalize several classical results on the integrability of trigonometric series and relations among the best approximation and the coefficients of trigonometric series.Theorem 3 and Theorem 4 are the first result...We generalize several classical results on the integrability of trigonometric series and relations among the best approximation and the coefficients of trigonometric series.Theorem 3 and Theorem 4 are the first results on the relations among the weighted best approximation and the coefficients of trigonometric series.展开更多
A class of nonidentical parallel machine scheduling problems are considered in which the goal is to minimize the total weighted completion time. Models and relaxations are collected. Most of these problems are NP-hard...A class of nonidentical parallel machine scheduling problems are considered in which the goal is to minimize the total weighted completion time. Models and relaxations are collected. Most of these problems are NP-hard, in the strong sense, or open problems, therefore approximation algorithms are studied. The review reveals that there exist some potential areas worthy of further research.展开更多
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
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
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
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
In this paper we investigate weighted polynomial approximations with several variables. Our study relates to the approximation for by weighted polynomial. Then we will give some results relating to the Lagrange interp...In this paper we investigate weighted polynomial approximations with several variables. Our study relates to the approximation for by weighted polynomial. Then we will give some results relating to the Lagrange interpolation, the best approximation, the Markov-Bernstein inequality and the Nikolskii- type inequality.展开更多
In this survey the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the LP spaces and recent results in Orlicz spaces. The notion of balanced point, introduced by Ch...In this survey the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the LP spaces and recent results in Orlicz spaces. The notion of balanced point, introduced by Chui et al. in 1984 are extensively used.展开更多
In this survey, the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the LP spaces and recent results in Orlicz spaces. The notion of balanced point, which was intro...In this survey, the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the LP spaces and recent results in Orlicz spaces. The notion of balanced point, which was introduced by Chui et al. in 1984 are extensively used.展开更多
文摘We study certain weighted Bergman and weighted Besov spaces of holomorphic functions in the polydisk and in the unit ball.We seek conditions on the weight functions to guarantee that the dilations of a given function converge to the same function in norm;in particular,we seek conditions on the weights to ensure that the analytic polynomials are dense in the space.
文摘In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and G(z)=∑^(N)_(i)=1 A_(−i)z^(i),A_(i)ae culants.
基金Under the auspices of the National Natural Science Foundation of China(No.42271224,41901193)Ministry of Edu cation Humanities and Social Sciences Research Planning Fund Project of China(No.24YJAZH190)+1 种基金Anhui Province Excellent Youth Research Project in Universities(No.2022AH030019)Anhui Social Sciences Innovation Development Research Project(No.2024CXQ503)。
文摘The accessibility of urban public transit directly influences residents’quality of life,travel behavior,and social equity.Its correlation with housing prices has garnered significant attention across disciplines such as geography,economics,and urban planning.Although much existing research focuses on the impact of individual transportation facilities on housing prices,there is a notable gap in comprehensive analyses that assess the influence of overall urban transit accessibility on housing market dynamics.This study selected the main urban area of Hefei,China,as a case to investigate the spatial distribution of housing prices and evaluate public transit accessibility in 2022.Employing techniques such as the optimized parameter geographical detector and local spatial regression models,the study aimed to elucidate the effects and underlying mechanisms of urban transit accessibility on housing prices.The findings revealed that:1)housing prices in Hefei exhibited a clustered spatial pattern,with high prices concentrated in the city center and lower prices in peripheral areas,forming three distinct high-price hotspots with a‘belt-like’distribution;2)public transit accessibility showed a‘coreperiphery’structure,with accessibility declining in a‘circumferential’pattern around the city center.Based on the‘housing price-accessibility’dimension,four categories were identified:high price-high accessibility(37.25%),high price-low accessibility(19.07%),low price-high accessibility(21.95%),and low price-low accessibility(21.73%);3)the impact of transit accessibility on housing prices was spatially heterogeneous,with bus travel showing the strongest explanatory power(0.692),followed by automobile,subway,and bicycle travel.The interaction of these transportation modes generated a synergistic effect on housing price differentiation,with most influencing factors contributing more than 25%.These findings offer valuable insights for optimizing the spatial distribution of public transit infrastructure and improving both urban housing quality and residents’living standards.
文摘The paper gives a new way of constructing Hermite Fejer and Hermite interpolatory polynomials with the nodes of the roots of first kind of Chebyshev polynomials and gives the approximation order of these two kinds of operators. The approximation orders are described with the best rate of approximation of f by polynomials of degree N=(q+1)n 1 in L p w spaces.
文摘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.
文摘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）.
基金This work is supported by Universidad Nacional de Rio Cuarto.
文摘In this paper we establish a result about uniformly equivalent norms and the convergence of best approximant pairs on the unitary ball for a family of weighted Luxemburg norms with normalized weight functions depending on ε, when ε→ 0. It is introduced a general concept of Pade approximant and we study its relation with the best local quasi-rational approximant. We characterize the limit of the error for polynomial approximation. We also obtain a new condition over a weight function in order to obtain inequalities in Lp norm, which play an important role in problems of weighted best local Lp approximation in several variables.
文摘In the present paper, we establish direct and converse theorems for weight-ed Bernstein-Durrmeyer operators under weighted L^p-norm with Jacobi weight w（x）=x^a（1-x）β.All the results involved have no restriction a,β〈1-1/p,which indicates that the weighted Bemstein-Durrmeyer operators have some better approxi- mation properties than the usual Bernstein-Durrmeyer operators.
文摘We prove some approximation properties of generalized Meyer-Konig and Zeller operators for differentiable functions in polynomial weighted spaces. The results extend some results proved in [1-3,7-16].
文摘The author consides Beta operators βnf on suitable Sobolev type subspace of Lp[0, ∞) and characterizes the global rate of approximation of derivatives f(r) through corresponding derivatives (βnf)(r) in an appropriate weighted Lp-metric by the rate of Ditzian and Totik's r-th order weighted modulus of Smoothness.
文摘We generalize several classical results on the integrability of trigonometric series and relations among the best approximation and the coefficients of trigonometric series.Theorem 3 and Theorem 4 are the first results on the relations among the weighted best approximation and the coefficients of trigonometric series.
基金the National Natural Science Foundation of China (70631003)the Hefei University of Technology Foundation (071102F).
文摘A class of nonidentical parallel machine scheduling problems are considered in which the goal is to minimize the total weighted completion time. Models and relaxations are collected. Most of these problems are NP-hard, in the strong sense, or open problems, therefore approximation algorithms are studied. The review reveals that there exist some potential areas worthy of further research.
文摘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.
文摘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.
基金Supported by the Zhejiang Provincial Natural&Science Foundation
文摘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.
文摘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.
文摘In this paper we investigate weighted polynomial approximations with several variables. Our study relates to the approximation for by weighted polynomial. Then we will give some results relating to the Lagrange interpolation, the best approximation, the Markov-Bernstein inequality and the Nikolskii- type inequality.
文摘In this survey the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the LP spaces and recent results in Orlicz spaces. The notion of balanced point, introduced by Chui et al. in 1984 are extensively used.
文摘In this survey, the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the LP spaces and recent results in Orlicz spaces. The notion of balanced point, which was introduced by Chui et al. in 1984 are extensively used.
