Suppose that the outer mapping function of domain D has its second continuous derivatives. In this paper, the order proximation by (0,1,…,q) Hermite-Fejer interpolating polynomials at nearly Fejer's points of fun...Suppose that the outer mapping function of domain D has its second continuous derivatives. In this paper, the order proximation by (0,1,…,q) Hermite-Fejer interpolating polynomials at nearly Fejer's points of function of class A(D) are presented. Moreover in general the order of approximation is sharp.展开更多
The paperintroduces Herm ite-Fejértype(Herm ite type) interpolation ofhigherorder denoted by Smn (f)(Sm n(f)), and gives som e basic properties including expression form ulas, convergence relationship betw een ...The paperintroduces Herm ite-Fejértype(Herm ite type) interpolation ofhigherorder denoted by Smn (f)(Sm n(f)), and gives som e basic properties including expression form ulas, convergence relationship betw een Sm n(f) and Hmn(f) (Herm ite-Fejérinterpolation ofhigheror- der), and the saturation ofSmn(f).展开更多
For the nonpositive Hermite-Fejér interpolation based on the Laguerre abscissas, a pointwise two-sided estimate of the degree of approximation in the aleatoric interval [0, A] is first established.
In this paper sufficient conditions for mean convergence and rate of convergence of Hermite-Fejer type interpolation in the Lp norm on an arbitrary system of nodes are presented.
L' convergence of Hermite-Fejer interpolation and quasi-Hermite-Fejer interpolation based upon ze- ros of general orthogonal polynomials is investigated. This paper 'almost' characterizes such convergence ...L' convergence of Hermite-Fejer interpolation and quasi-Hermite-Fejer interpolation based upon ze- ros of general orthogonal polynomials is investigated. This paper 'almost' characterizes such convergence for all continuous functions.展开更多
In this paper we introduce a new kind of the mixed Hermite--Fejér interpolation with boundary condi- tions and obtain the mean approximation order.Our results include a new theorem of Varma and Prasad.Be- sides,w...In this paper we introduce a new kind of the mixed Hermite--Fejér interpolation with boundary condi- tions and obtain the mean approximation order.Our results include a new theorem of Varma and Prasad.Be- sides,we also get some other results about the mean approximation.展开更多
This article is a improvement on author＇s early work （Acta Mathematica Scientia, Vol.30 No.2 Ser.A 2010）. In this article, there are two new contributions： 1） The restrictive conditions on approximation domain bo...This article is a improvement on author＇s early work （Acta Mathematica Scientia, Vol.30 No.2 Ser.A 2010）. In this article, there are two new contributions： 1） The restrictive conditions on approximation domain boundary is improved essentially. 2） The Fejer points is extended by perturbed Fejer points with stable order of approximation.展开更多
The 'o' saturation theorem and the degree of Lwp, approximation by (0 - q' - q) type Hermite-Fejer interpolating polynomials for mean convergence are obtained.
The object of this paper is to show regularity of(0,1,...,r-2,r) interpolation on the set obtained by projecting vertically the zeros of (1-x2)pn(x)(λ≥1/2)onto the unit circle,where Pn(x)stands for the nth ultrasphe...The object of this paper is to show regularity of(0,1,...,r-2,r) interpolation on the set obtained by projecting vertically the zeros of (1-x2)pn(x)(λ≥1/2)onto the unit circle,where Pn(x)stands for the nth ultraspherical polynomial.展开更多
文摘Suppose that the outer mapping function of domain D has its second continuous derivatives. In this paper, the order proximation by (0,1,…,q) Hermite-Fejer interpolating polynomials at nearly Fejer's points of function of class A(D) are presented. Moreover in general the order of approximation is sharp.
文摘The paperintroduces Herm ite-Fejértype(Herm ite type) interpolation ofhigherorder denoted by Smn (f)(Sm n(f)), and gives som e basic properties including expression form ulas, convergence relationship betw een Sm n(f) and Hmn(f) (Herm ite-Fejérinterpolation ofhigheror- der), and the saturation ofSmn(f).
基金Supported by Science and Research Fund Item of Education Department of Zhejiang Province(20050408).
文摘For the nonpositive Hermite-Fejér interpolation based on the Laguerre abscissas, a pointwise two-sided estimate of the degree of approximation in the aleatoric interval [0, A] is first established.
基金Project 19671082 supported by National Natural Science Foundation of China, I acknowledge endless help from Prof. Shi Ying-Guang during finishing this paper.
文摘In this paper sufficient conditions for mean convergence and rate of convergence of Hermite-Fejer type interpolation in the Lp norm on an arbitrary system of nodes are presented.
基金Supported by the National Natural Science Foundation of China.
文摘L' convergence of Hermite-Fejer interpolation and quasi-Hermite-Fejer interpolation based upon ze- ros of general orthogonal polynomials is investigated. This paper 'almost' characterizes such convergence for all continuous functions.
文摘In this paper we introduce a new kind of the mixed Hermite--Fejér interpolation with boundary condi- tions and obtain the mean approximation order.Our results include a new theorem of Varma and Prasad.Be- sides,we also get some other results about the mean approximation.
基金supported by NSF of Henan Province P. R. China(974050900)
文摘This article is a improvement on author＇s early work （Acta Mathematica Scientia, Vol.30 No.2 Ser.A 2010）. In this article, there are two new contributions： 1） The restrictive conditions on approximation domain boundary is improved essentially. 2） The Fejer points is extended by perturbed Fejer points with stable order of approximation.
基金This work is supported by the Doctor Foundation (No:02.T20102-06) and the Post Doctor Foundation of Ningbo University.
文摘The 'o' saturation theorem and the degree of Lwp, approximation by (0 - q' - q) type Hermite-Fejer interpolating polynomials for mean convergence are obtained.
文摘The object of this paper is to show regularity of(0,1,...,r-2,r) interpolation on the set obtained by projecting vertically the zeros of (1-x2)pn(x)(λ≥1/2)onto the unit circle,where Pn(x)stands for the nth ultraspherical polynomial.
