一类推广的Bernstein-Kantorovich算子的点态逼近

讨论Bernstein-Kantorovich算子的一种推广形式的逼近性质,运用插项的方法证明了逼近正定理,并证明了逆定理,得到了逼近等价定理.完善了算子在逼近性质方面的结果.     

插补空间的逼近外推定理

本文建立了拟模Abelian群上双参数算子族逼近的外推定理,所得的结果包含了DeVoreR．等人对正规逼近族之最佳逼近所建立的外推定理,且所需的条件更弱．同时从本文的结果立即可以建立起算子逼近的外推定理．     

关于多值函数的逼近问题

本文讨论了多值函数的逼近问题,得到关于非凸值多值函数的两个逼近定理,Cellina逼近定理和De Blasi-Myjak逼近定理被作为推论重新得到,最后,作为应用,证明了一个抽象经济模型的均衡存在性定理.     

关于weierstrass逼近定理的几点注记

Weierstrass逼近定理是函数逼近论中的重要定理之一,定理阐述了闭区间上的连续函数可以用一多项式去逼近.将该定理进行推广:即使一个函数是几乎处处连续的,也不一定具有与连续函数相类似的逼近性质,但是一个处处不连续的函数却有可能具有这样的性质.证明了定义在闭区间上且与连续函数几乎处处相等的函数具有类似的逼近性质,并给出了weierstrass逼近定理的一个推广应用.     

双连续n次积分C余弦函数的逼近定理

基于双连续半群概念,引入一致双连续半群序列概念,借助Laplace变换和Trotter-Kato定理,考察双连续n次积分C余弦函数与C-预解式之间的关系,得到逼近定理的稳定性条件,进而得出双连续n次积分C余弦函数逼近定理.从而对Banach空间强连续半群逼近定理和双连续半群逼近定理进行了推广,为相应抽象的Cauchy问题提供了解决方案.     

Characterization of best uniform approximation with restricted ranges of derivatives

This paper gives a general characterization theorem of a best uniform approximation of generalized polynomial having multiple restricted ranges of its derivatives. This theorem is widely applicable. The results on characterization in many standard approximations, such as approximation with Hermite-Birkhoff interpolatory side conditions, multiple comonotone approximation, and approximation by algebraic polynomials having bounded coefficients, etc., are special cases of our results.     

Discrete one-sided nonlinear Lp approximation

Under the local Haar condition, an interpolatory theorem for discrete one-sided nonlinear L_p (p>1) approximation is obtained. Under the strong Young’s condition, a Polya-type theorem with discretization for one-sided nonlinear approximation and a limit (discretization) theorem for one-sided modified L_p (p≥1) approximation are given.     

Approximation by Bézier variants of the BBHK operators

In this work a new type of approximation operator—the Bézier variant of the BBHK operator—is introduced. Its approximation properties are studied. A convergence theorem for such approximation operators for locally bounded functions is established by means of some techniques of probability theory and analysis methods. This convergence theorem subsumes the approximation of functions of bounded variation as a special case.     

Properties of Convergence for a Class of Generalized $q$-Gamma Operators.

In this paper, a generalization of $q$-Gamma operators based on the concept of $q$-integer is introduced. We investigate the moments and central moments of the operators by computation, obtain a local approximation theorem and get the pointwise convergence rate theorem and also obtain a weighted approximation theorem. Finally, a Voronovskaya type asymptotic formula was given.     

Bernstein-Sikkema算子逼近

研究Ｂｅｒｎｓｔｅｉｎ－Ｓｉｋｋｅｍａ算子的逼近问题,得到强型正定理和弱型逆定理,改进了文献［１］的结果     

Pointwise simultaneous approximation for Baskakov quasi-interpolants

Recently P. Mache and M. W. Müller introduced the Baskakov quasi-interpolants and obtained an approximation equivalence theorem. In this paper we consider simultaneous approximation equivalence theorem for Baskakov quasi-interpolants.     

Convergence and approximation of semigroups of Lipschitz operators

A convergence theorem and an approximation theorem for semigroups of Lipschitz operators are given. These theorems are applied to a semi-discrete approximation problem for a quasi-linear wave equation with damping and a finite difference method for a quasi-linear equation of Kirchhoff type.     

泛函中的两个对偶定理

本文利用＊隔离定理,证明了Ｍａｚｕｒ定理和凸集的最佳逼近元存在性定理的对偶定理．     

On the Element of Best Nonsymmetric Approximation in Spaces with Nonsymmetric Quasinorm

In this paper, we prove an existence theorem for the element of best nonsymmetric approximation in spaces with nonsymmetric quasinorm. Examples showing the importance of the conditions embodied in the theorem are presented. A criterion for determining the element of best nonsymmetric approximation is given.     

CHEBYSHEV APPROXIMATION BY FUNCTIONS HAVING RESTRICTED RANGES WITH EQUALITIES

In this paper, we establish a new type of alternation theory for more general restricted ranges Chebyshev approximation with equalities. The uniqueness and strong uniqueness theorems are given. Applying the results, we obtain the alternation theorem and uniqueness theorem for best coposilive approximation.     

A KY FAN MATCHING THEOREM FOR TRANSFER COMPACTLY OPEN COVERS AND THE APPLICATION TO THE FIXED POINT

In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type fixed point theorem are obtained.     

A KY FAN MATCHING THEOREM FOR TRANSFER COMPACTLY OPEN COVERS AND THE APPLICATION TO THE FIXED POINT

In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type fixed point theorem are obtained.     

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.     

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.