A Characterization of Pointwise Approximation for Linear Combinations of Szász-type Operators

In this paper, we use Ditzian-Totik modulus to study the pointwise approximation for the linear combinations of Szasz-type operators, and obtain the direct and converse theorem and the characterization of the pointwise approximation for the linear combinations of Szasz-type operators.     

推广的Kantorovich算子在Ba空间中的逼近

利用Ditzian-Totik光滑模,研究了推广的Kantorovich算子在Ba空间中的逼近,得到逼近的正定理与等价定理.所得结果改进、推广和统一了一些作者的结果.     

Equivalence theorem on weighted simultaneous Lp-approximation by means of Szasz-Kantorovich operators and Baskakov-Kantorovich operators

The intention of this paper is to give direct and converse results on weighted simultaneous approximation by means of Szász-Kantorovich operators and Baskakov-Kantorovich operators in L_p-norms using the weighted Ditzian-Totik modulus of smoothness. Supported by the foundation of Zhejiang province     

Kantorovich算子在Ba空间中的逼近

利用Ditzian-Totik光滑模,研究了Kantorovich算子在Ba空间中的逼近.得到逼近的正定理与等价定理.所得结果改进,推广和统一了一些作者的结果.     

Sz\''asz-Kantorovich-B\''{e}zier算子在$L_p[0, \infty)$上的逼近定理

本文利用Ditzian-Totik模得到了Sz\'{a}sz-Kantorovich-B\'{e}zier算子在$L_{p}[0,\infty)$空间逼近的正逆定理及等价定理.     

THE GLOBAL APPROXIMATION BY LEFT-BERNSTEIN-DURRMEYER QUASI-INTERPOLANTS IN Lp[0,1]

In this paper, we will use the 2r-th Ditzian-Totik modulus of smoothness wψ2r(f,t)p to discuss the direct and inverse theorem of approximation by Left-Bernstein-Durrmeyer quasi-interpolants Mn[2r-1]f for functions of the space Lp[0,1] (1≤ p≤ +∞).     

Direct and converse theorems of the theory of approximation in the metric of Lp for 0 < p < 1

A direct theorem of the Jackson type and several converse theorems are established for the approximation of periodic functions of period 2Π by trigonometrical polynomials in the metric of L_p, 0 < p < 1.     

Lp空间Shepard算子逼近的正逆定理

本文引入了一种修正的积分型Shepard算子,建立了相应的Jackson型定理,并通过建立Bernstein型不等式,给出了算子在L[0,1]p空间中一种新的逼近阶刻画的等价形式,得到了逼近的逆定理．     

Pointwise Approximation by Szàsz-Mirakjan Quasi-Interpolants

Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence. A.T. Diallo investigated some approximation properties of Szàsz-Mirakjan Quasi-Interpolants, but he obtained only direct theorem with Ditzian-Totik modulus ω2rψ(f, t). In this paper, we extend Diallo's result and solve completely the characterization on the rate of approximation by the method of quasi-interpolants to functions f ∈ CB[0, ∞) by making use of the unified modulus ω2rψλ> (f, t) (0 ≤λ≤ 1).     

Baskakov型算子同时逼近的点态估计

In this paper, for Baskakov, Baskakov-Kantorovich and Baskakov-Durrmyer operators Ln(f,x),we give a simultaneous approximation of equivalent theorem with ω^2ψλ (f, t) The theorem unites the corrosponding results of classical and the Ditzian-Totik moduli of smoothness.     

Uncertainty Principles for the Generalized Fourier Transform Associated with Spherical Mean Operator

The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.     

Baskakov-Durrmeyer算子的点态逼近

本应用Ditzian-Totik模得到Baskakov-Durrmeyer算子线性组合的点态逼近的等价定理。     

广义Baskakov型算子的强逆不等式

利用二阶Ditzian-Totik模考虑一类算子的强逆不等式，这类不等式曾经被许多者用不同的方法研究过。本文将采用一种统一的方法来处理一大类算子的强逆不等式，得到了它们的Ditzian-Ivanov结果。本方法适用于更广的算子。     

Baskakov-Durrmeyer算子的点态逼近

本文应用Ｄｉｔｚｉａｎ－Ｔｏｔｉｋ模得到Ｂａｓｋａｋｏｖ－Ｄｕｒｒｍｅｙｅｒ算子线性组合的点态逼近的等 价定理．     

Sz\`{a}sz-Mirakjan 算子拟中插式的点态逼近等价定理

Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence. A.T. Diallo investigated some approximation properties of Szasz-Mirakjan Quasi-Interpolants, but he obtained only direct theorem with Ditzian-Totik modulus wφ^2r （f, t）. In this paper, we extend Diallo＇s result and solve completely the characterization on the rate of approximation by the method of quasi-interpolants to functions f ∈ CB[0, ∞） by making use of the unified modulus wφ^2r（f, t） （0≤λ≤ 1）.     

Lp空间有理插值型算子的逼近

考虑了两类有理插值型算子的Jackson型估计．当p〉1时．建立了Dilzian—Totik型定理，当p=1时．利用通常连续模给出了Jackson型估计．     

Liouville type theorems for a system of integral equations on upper half space

In this paper,we consider the following system of integral equations on upper half space {u(x) = ∫Rn + (1/|x-y|n-α-1/|-y|n-α) λ1up1(y) + μ1vp2(y) + β1up3(y)vp4(y) dy;v(x) = ∫Rn + (1/|x-y|n-α-1/|-y|n-α)(λ2uq1(y) + μ2vq2(y) + β2uq3(y)vq4(y) dy,where Rn + = {x =(x1,x2,...,xn) ∈ Rn|xn 0}, =(x1,x2,...,xn-1,-xn) is the reflection of the point x about the hyperplane xn= 0,0 α n,λi,μi,βi≥ 0(i = 1,2) are constants,pi≥ 0 and qi≥ 0(i = 1,2,3,4).We prove the nonexistence of positive solutions to the above system with critical and subcritical exponents via moving sphere method.     

APPROXIMATION BY A CLASS OF MODIFIED SZASZ-DURRMEYER OPERATORS

ThisprojectissupportedbyZhejiangProvincialFoundationofChina.1.IntroductionForjEC[0,1]ther-thBernsteinpolynomialisdefinedbyItwasshownbyH.BerensandG.G.Lorentz([2]in1972)thatif0相似文献   

Bernstein型算子线性组合加Jacobi权逼近及高阶导数的等价定理

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.     

Asymptotic Property of Approximation to xαgnx by Newman Type Operators

The approximation of ｜x｜ by rational functions is a classical rationalproblem. This paper deals with the rational approximation of the function xasgnx, which equals ｜x｜ if α=1. We construct a Newman type operator rn（x） and show max｜x｜≤1{｜x^αsgnx-rn（x）｜}-Cn-α/2e-√2nα where C is a constant depending on α.