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.     

用算子逼近周期连续函数

<正> 我们知道当ρ_k~(n)≡1时,U_n(f,x)即为富里埃级数的部份和;又若u_n(t)≥0(0≤t≤2π),那末U_n(f,x)即所谓线性正算子,关于正算子的逼近问题,文[1]和[2]都作了详细的讨论,其中有这样的一个结果(参阅[1]第73页定理14):     

单纯形上积分型Stancu算子对连续函数的逼近

本文首先构造了单纯形上积分型Stancu算子,其讨论了它对连续函数的逼近,运用Mamedov-Shisha和Devore-Freud量化方法,得到了该算子对连续函数及连续可微函数的逼近度,并给出它的Vonorovskya型渐近公式。     

ON INTERPOLATION AND APPROXIMATION BY RATIONAL FUNCTIONS WITH PREASSIGNED POLES

<正> 1. INTRODUCTION. It is the purpose of this paper to presentsome results,on the problem of interpolation and approximation toa functiou f(z),analytic on a closed limited point set E in thecomplex z-plane whose complement K is connected and regular inthe sense that Green's fumction for K exists,by rational functionsf_n(z) of respective degrees n,n=1,2,…of the form     

一种广义周期Besov类的多元周期多项式样条逼近

本文证明多元多项式周期样条空间是某些多元周期光滑函数类的关于Kolmogorov n-宽度的弱渐近极子空间．给出了广义周期Besov类的一种推广，得到了空间元素的一种表示定理，不仅给出了一种多元周期多项式样条算子．而且证明了所得的结果．     

用广义多项式逼近在正数轴上的函数

<正> 导言伯恩斯坦曾经证明:设 F(x)是偶的整函数,其泰勒系数不是负数,并且它的性(род,genus)大于零.如果 f(x)在(—∞,∞)上连续,并且适合     

ENTIRE FUNCTIONS REPRESENTED BY LAPLACE-STIELTJES TRANSFORMS CONCERNING THE APPROXIMATION AND GENERALIZED ORDER

The first aim of this paper is to investigate the growth of the entire function defined by the Laplace-Stieltjes transform converges on the whole complex plane. By introducing the concept of generalized order, we obtain two equivalence theorems of Laplace-Stieltjes transforms related to the generalized order, A_n~*and λ_n. The second purpose of this paper is to study the problem on the approximation of this Laplace-Stieltjes transform. We also obtain some theorems about the g...     

拟凸函数与切比晓夫逼近

木文第一节给出拟凸函数和显拟凸函数(explicitly quasiconvex functions)的一个新的特征;同时引进一种新的凸性——我们称它为强伪凸性,并给出它的若干重要性质.第二节讨论第一节的结果在最佳一致逼近中的应用,建立了交错定理、唯一性定理和强唯一性定理.     

关于连续函数与可微函数的共凸逼近

关于凸逼近,共凸逼近的各种逼近阶的估计在近十多年来已引起了相当的重视和较多的研究,因为保形渐近的思想在实际问题中有着十分重要的意义。相比较而言,共凸逼近的的研究比凸逼近的情况要复杂,因此,不少关于凸逼近已得到解决的问题对于共凸逼近仍没有结果,关于共凸逼近,1984,Atacir,Sermin证明了。     

多元正系数代数多项式倒数对非负连续函数的逼近

设d≥1为正整数,S为Rd中的单纯形,C(S)为S上的连续函数类,f(x)∈C(S),f(x)≥0,f≠0,则文中证明存在Pn(x)∈Ⅱ+n,d={Pn(x)=∑|k|≤n akxk(1-|x|)n-|k|x∈S,ak≥ 0},绝对常数C＞0使||f-1/Pn||≤C[ωψ(f,1/√n)+||f||/√n],这里k,x∈Rd,k=(k1,k2,…,kd),x=(x1,x2,…,xd),|k|=k1+k2+…+kd,|x|=x1+x2+…+xd,xk=x1k1x2k2…xdkd,ωψ(f,t)为单纯形S上的一阶Ditzian-Totik光滑模,||f||=maxx∈S|f(x)|.     

代数多项式和指数型整函数在Besov空间中的逼近

用Ｋ－泛函定义了一类Ｂｅｓｏｖ空间,并分别用ｎ阶代数多项式及指数为σ的整函数的最佳逼近阶给出了其特征的刻画。     

ASYMPTOTIC APPROXIMATION OF FUNCTIONS AND THEIR DERIVATIVES BY GENERALIZED BASKAKOV-SZ(A)ZS-DURRMEYER OPERATORS

We present the complete asymptotic expansion for a generalization of the Baskakov-Szasz-Durrmeyer operators and their derivatives.     

VECTOR-VALUED HOLOMORPHIC FUNCTIONS ON THE COMPLEX BALL AND THE ANALYTIC RADON-NIKODYM PROPERTY

1IntroductionAcomplexBanachspacewithvaluesinwhicheveryboundedallalyticfunctionontheopenunitdiskhasradialliniltsatalmostallboundarypointsissaidtohavetheanalyticRa.don-NikodympropertyApaPerofBukhvalovandDanilevich[5lexanlinesthistopic.TheclassofBanachspaceswiththeanalyticRadon-Niliodympropertyisslightlylargerthanthatwiththeffedon-NikodympropertyIndeed,itisshownill[5]thatL1andmoregenerallyallBanachlatticesnotcontainingcoalsoverifytheanalyticffedon-NikodympropertyAftertheirwork,severalchaJra…     

Cn单位球上的向量值Dpμ,q函数

讨论了Cn单位球上的向量值Dpμ,q函数, 利用Banach空间几何学的方法,推广了标量值Dpμ,q函数的结果.     

Г-CONVERGENCE OF INTEGRAL FUNCTIONALS DEPENDING ON VECTOR-VALUED FUNCTIONS OVER PARABOLIC DOMAINS

This paper studies Г-convergence for a sequence of parabolic functionals, F^e(u)=∫0^T∫f(x/e,t.Δ↓u) dxdt as ε→0, where the integrand f is nonconvex, and periodic on the first variable. The author obtains the representation formula of the Г-limit. The results in this paper support a conclusion which relates Г-convergence of parabolic functionals to the associated gradient flows and confirms one of De Giorgi‘s conjectures partially.     

样条函数变差缩减逼近法的迭代极限

本文是[1]的进一步推广,即把[1]中所考虑的三次等距节点的样条函数推广为任意(非等距)节点与任意幂次的多项式样条函数情形.对于最一般的多项式样条函数,我们证明了它的变差缩减逼近法当其迭代次数趋于无穷时也是收敛的,并且它的极限函数由折线多边形所组成(详见本文定理3).     

关于Baskakov-Durrmeyer算子的局部逼近

本文主要讨论了用Ｈｏｌｄｅｒ连续函数表示Ｂａｓｋａｋｏｖ－Ｄｕｒｒｍｅｙｅｒ算子局部逼近阶的特征刻划问题。     

伪多元函数的Padé型逼近

给出伪多元函数的Pad\'{e}型逼近,其优点在于:简化了多元函数有理逼近的计算,加速了函数在奇点处的收敛.并讨论其性质以及误差分析.