多元Kantorovich算子的最优逼近类

本文研究定义在单纯形上的多元Kantorovich算子逼近的正逆不等式与饱和定理,给出该算子在Lp(1≤p≤∞)空间的最优逼近类,即利用K-泛函的特征刻画分别满足‖Knf-f‖p=O(n-1) 与‖Knf-f‖p=o(n-1)的函数类．     

Approximation Properties of Two-Dimensional q-Bernstein-Chlodowsky-Durrmeyer Operators

This article deals with the Durrmeyer-type generalization of the q-Bernstein-Chlodowsky operators on a rectangular domain (which were introduced by Büyükyaz?c? [2 ?. Büyükyaz?c? ( 2009 ). On the approximation properties of two-dimensional q-Bernstein-Chlodowsky polynomials . Math. Commun. 14 : 255 – 269 .[Web of Science ®] , [Google Scholar]]). We obtain the Korovkin-type approximation properties and the rates of convergence of this generalization using the means of the modulus of continuity and using the K-functional of Peetre. Further, we establish the weighted approximation properties for these operators.     

Approximation by Means of Kantorovich-Stancu Type Operators

The purpose of this article is to give a Kantorovich generalization of Stancu type polynomials. We obtain convergence properties of our operators in the continuous function space and Lebesgue spaces. Furthermore, we get the order of approximation with the help of modulus of continuity and give a numerical example for approximation.     

Some Approximation Properties of Certain q-Baskakov-Beta Operators

In this paper, we propose the q analogue of modified Baskakov-Beta opera-tors. 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.     

Bernstein型算子同时逼近误差

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.     

Shepard-Lagrange算子的逼近

本文建立了Shepard-Lagrange算子逼近的正逆定理,证明了可以利用高阶光滑模来刻画Shepard-Lagrange算子的逼近性质.从而说明了Shepard-Lagrange算子比一般的Shepard算子具有更好的逼近性质.进一步,所用光滑模的阶梯函数非常广泛,这是多项式逼近所不具有的.     

Approximation Properties For Modified q-Bernstein-Kantorovich Operators

The purpose of this article is to give a generalization of q-Bernstein-Kantorovich operators. We present some approximation theorems. We compute the rate of convergence and error estimation of these operators by means of the modulus of continuity. Furthermore, we give some numerical examples to show comparisons in illustrative graphics for the convergence of these operators to various functions.     

多元Bernstein—Durrmeyer算子的正逆定理

本文给出单形Ｓ上多元Ｂｅｒｎｓｔｅｉｎ－Ｄｕｒｒｍｅｙｅｒ算子在连续函数空间Ｃ（Ｓ）的强型正定理的积分型估计式弱型逆定理从而建立了算子逼近特征刻划等价定理。     

Approximation by polynomials and rational functions in weighted rearrangement invariant spaces

Let Γ be a Dini-smooth curve in the complex plane, and let G:=IntΓ. We prove some direct and inverse theorems of approximation theory by algebraic polynomials and rational functions in the weighted rearrangement invariant Smirnov spaces EX(G,ω) defined on G.     

Approximation by Durrmeyer–Bezier operators

In the present paper, we consider the Bezier variant M_n,α(f,x) of the generalized Durrmeyer type operators, and obtain an estimate on the rate of convergence of M_n,α(f,x) for the decomposition technique of functions of bounded variation. In the end we propose an open problem for the readers and give an asymptotic formula for these generalized Durrmeyer type operators.     

On Certain Best Constants for Bernstein-Type Operators

We discuss the generalized version of a best-constant problem raised by Z. Li in a note which recently appeared in Journal of Approximation Theory. Some best constants for well known Bernstein-type operators are obtained.     

On Certain Positivity Classes of Operators

A real square matrix A is called a P-matrix if all its principal minors are positive. Such a matrix can be characterized by the sign non-reversal property. Taking a cue from this, the notion of a P-operator is extended to infinite dimensional spaces as the first objective. Relationships between invertibility of some subsets of intervals of operators and certain P-operators are then established. These generalize the corresponding results in the matrix case. The inheritance of the property of a P-operator by the Schur complement and the principal pivot transform is also proved. If A is an invertible M-matrix, then there is a positive vector whose image under A is also positive. As the second goal, this and another result on intervals of M-matrices are generalized to operators over Banach spaces. Towards the third objective, the concept of a Q-operator is proposed, generalizing the well known Q-matrix property. An important result, which establishes connections between Q-operators and invertible M-operators, is proved for Hilbert space operators.     

On a Double Complex Sequence of Linear Operators

The main goal of the article is to introduce a class of double complex linear operators of integral type. The technique is based by extension into the complex domain of a real positive approximation process. Involving the first modulus of continuity, we investigate their geometric and approximation properties. The statistical convergence of our sequence is proved. In a particular case, our operators turn into the double complex Gauss-Weierstrass integral operators.     

On Convergence Properties for a Class of Kantorovich Discrete Operators

Here we give some pointwise convergence theorems and asymptotic formulae of Voronovskaja type for a general class of Kantorovich discrete operators. Applications to the Kantorovich version of some discrete operators are given.     

On Approximation Properties of Generalized q-Bernstein Operators

In this study, we identify a generalization of q-Bernstein type operators and investigate approximation properties of a sequence of these operators . We estimate rate of approximation by modulus of continuity. We prove Voronovskaya type theorem for these operators.     

对于局部有界函数的积分型Szász-Bézier算子的逼近估计

引入一种积分型的 Szász- Bézier算子 ,并研究其逼近性质 ,得到了此类算子对局部有界函数的逼近阶估计公式     

Baskakov算子线性组合的点态估计

本文利用Ditizian-Totik模给出Baskakov算子线性组合点态和整体逼近正逆定理的统一形式,得到了较高的逼近阶,并且刻画了该线性组合算子的逼近特征。     

On Certain Densely Invariant Quantities of Linear Operators

Let L(X,Y) denote the class of linear transformations T:D(T) ? X → Y where X and Y are normed spaces. A quantity f is called densely invariant if for every system L(X, Y) and every operator T ? L(X,Y) we have f(T/E)= f(T) whenever E is a core of T. The density invariance of certain well known quantities is established. In case Y is complete and T is closable, a stronger property is shown to hold for some of these quantitites, namely invariance under restriction to dense subspaces.     

An Approximation Criterion for Essential Self-adjointness of Dirichlet Operators on Certain Banach Spaces

We establish an approximation criterion for essential self-adjointness of Dirichlet operators with nonconstant diffusion part on certain Banach spaces.     

算子摄动与谱值映射的连续性

讨论 Hibert空间上有界线性算子摄动和谱值映射的连续性问题 .得到 σk(.)一类子集上半连续的充要条件和 H∞∞ (.)连续的充要条件 ,推广了文 [7]主要结果 .