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STRONG UNIQUENESS OF GENERALIZED P0LYNOMIAL OF BEST approximation HAVING BOUNDED COEFFICIENTS

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Acta Mathematicae Applicatae Sinica 1991年第1期7卷 17-33页

作者： XU SHUSHENG Jiangnan University

Let the set of generalized polynomials haviug bounded coefficients be K={p=■a_(j)g_(j):α_(j)■[α_(j),β_(j)],j=1,2,…,n}where g_1,g_2,…,g_n are linearly independent continuous functions defined on the interval[a,b],α_(j)β_(j),are extended real numbers satisfyingα_(j)?andα_(j)≤β_(j).Assume that f is a continuousfunction defined on a compact set X[a,b].In the paper,we first give the sufficient conditions forthe polynomial of best uniform approxmation to f from K being unique and strongly ***,we give two forms of necessary and sufficient conditions for the best approximationto be strongly unique.

关键词： Continuous Function Real Number uniform approximation Math Application Generalize Polynomial

Jackson type theorems on complex curves

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Science China Mathematics 2009年第3期52卷 493-506页

作者： TU TianLiang Deptartment of Mathematics and Informatics, North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450011, China Deptartment of Mathematics and Informatics North China Institute of Water Conservancy and Hydroelectric Power Zhengzhou China

Let Γ be a closed smooth Jordan curve in the complex plane. In this paper, with the help of a class of fundamental functions of Hermite interpolation, the author introduces a continuous function interpolation which uniformly approximates to f(z) ∈ C(Γ ) with the same order of approximation as that in Jackson Theorem 1 on real interval [1, 1]. The accuracy of the order of approximation is proved. Using the method different from the early works, the author studies simultaneous approximation to function and its derivatives and the desired results analogues to that in Jackson Theorem 2 on real interval [1, 1] are obtained.

关键词： complex curves interpolation uniform approximation order of approximation 30E05 30E10 41A05 41A25 41A28

A New Third *** Interpolation Polynomial

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Chinese Quarterly Journal of Mathematics 1998年第4期13卷 10-16,页

作者：何甲兴李笑牛 Department of

In this paper,a new third type *** interpolation polynomial H n(f;x,r) with zeros of the Chebyshev ploynomial of the second kind is constructed. H n(f;x,r) converge uniformly on [-1,1] for any continuous function f(x)... 详细信息

关键词： uniform approximation the best convergence order Lagrange interpolation polynomial

On the uniform and Simultaneous approximations of Functions

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Advances in Pure Mathematics 2021年第10期11卷 785-790页

作者： Mansour Alyazidi Department of Mathematics King Saud University Riyadh Saudi Arabia

We consider the relation between the simultaneous approximation of two functions and the uniform approximation to one of these functions. In particular, F1 and F2 are continuous functions on a closed interval [a,b], S is an n-dimensional Chebyshev subspace of C [a,b] and s1* & s2* are the best uniform approximations to F1 and F2 from S respectively. The characterization of the best approximation solution is used to show that, under some restrictions on the point set of alternations of F1−s1* and F2−s2*, s1* or s2* is also a best A(1) simultaneous approximation to F1 and F2 from S with F1≥F2 and n=2.

关键词： Simultaneous approximation uniform approximation Relation Straddle Points Alternation

RATE OF CONVERGENCE FOR MEYER-KONIG AND ZELLER OPERATORS WITH JACOBI-WEIGHTS

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approximation Theory and Its Applications 2002年第3期18卷 52-64页

作者： SongRuying XuangPeicai 等 TaiyuanTeachersCollege China ShaoxingCollegeofArtsandScience China

We point out that the Meyer-Konig and Zeller operator Mn (f;x) are unbounded in usual Jacobi weighted norm at first, and then we consider the weighted approximation by Mn(f;x) by a new norm and obtain the characteriza... 详细信息

关键词： uniform approximation Weighted Sobolev Space Inverse Theorem Characterization Problem Youth Foundation

uniform Convergence of Extremal Polynomials When Domains Have Corners and Special Cusps on the Boundary

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Advances in Pure Mathematics 2011年第6期1卷 305-314页

作者： Cem Kosar Mehmet Kucukaslan Fahreddin G.Abdullayev Department of Mathematics Faculty of Science and LiteratureBitlis Eren UniversityBitlisTurkey Department of Mathematics Faculty of Science and LiteratureMersin UniversityMersinTurkey

We study the approximation properties of the extremal polynomials in Ap?norm and C?norm. We prove estimates for the rate of such convergence of the sequence of the extremal polynomials on domains with corners and spec... 详细信息

关键词： uniform approximation Extremal Polynomials Conformal Mapping p-Bieberbach Polynomials