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1.
Jia-Kai Li & Guo-Liang Xu 《计算数学(英文版)》1990,8(3):233-240
The aim of this conjoint paper is to discuss the problem of the best rational approximation with interpolating constraints. In part I, we give the necessary and sufficient conditions for the existence of the best rational approximations and establish some characterization theorem for such approximations. The problems of uniqueness, the properties for the set of best approximations, strong uniqueness and continuity of best approximation operator are considered in Part II. The results obtained in this paper are the completion and extension of those given in [1]. 相似文献
2.
李冲 《高等学校计算数学学报(英文版)》1993,(1)
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. 相似文献
3.
Shi Yingguang 《数学年刊B辑(英文版)》1983,4(2):227-230
In this paper the author discusses a problem of Chebyshev approximation by linear alternating families with fixed values at nodes and gives the analogues of all results for the classical Chebyshev approximation, which include the theorems on existence, alternation, uniqueness, strong uniqueness and the continuty of the best approximation operator, etc. 相似文献
4.
本文首先指出文献[1]中的一个错误,举例说明弱拟凸集的最佳逼近未必具有广义强唯一性,进而讨论两类共同逼近的强唯一性,在空间是一致凸、逼近集是共同太阳集的条件下,证明了最佳共同逼近具有广义强唯一性 相似文献
5.
罗先发 《高校应用数学学报(A辑)》2005,20(3):337-345
研究了复赋范空间中具限制系数的广义多项式集G对无穷序列的最佳同时逼近问题,得到了特征定理;当G是复RS集时还得到了惟一性定理. 相似文献
6.
Chandi Bhandari Ronald H.W. Hoppe Rahul Kumar 《Numerical Methods for Partial Differential Equations》2019,35(4):1477-1496
We prove the existence and uniqueness of a solution of a C0 Interior Penalty Discontinuous Galerkin (C0 IPDG) method for the numerical solution of a fourth‐order total variation flow problem that has been developed in part I of the paper. The proof relies on a nonlinear version of the Lax‐Milgram Lemma. It requires to establish that the nonlinear operator associated with the C0 IPDG approximation is Lipschitz continuous and strongly monotone on bounded sets of the underlying finite element space. 相似文献
7.
Riad Hassani Patrick Hild Ioan Ionescu 《Mathematical Methods in the Applied Sciences》2004,27(1):47-67
We consider the Signorini problem with Coulomb friction in elasticity. Sufficient conditions of non‐uniqueness are obtained for the continuous model. These conditions are linked to the existence of real eigenvalues of an operator in a Hilbert space. We prove that, under appropriate conditions, real eigenvalues exist for a non‐local Coulomb friction model. Finite element approximation of the eigenvalue problem is considered and numerical experiments are performed. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
8.
On Best Simultaneous Approximation 总被引:1,自引:0,他引:1
The problem is considered of best approximation of finite number of functions simultaneously. For a very general class of norms, characterization results are derived. The main part of the paper is concerned with proving uniqueness and strong uniqueness theorems. For a particular subclass, which includes the important special case of the Chebyshev norm, a characterization is given of a uniqueness element. 相似文献
9.
Pawe? Foralewski Alicja Szymaszkiewicz 《Journal of Mathematical Analysis and Applications》2008,345(1):410-419
Some criteria for extreme points and strong U-points in Cesàro-Orlicz spaces are given. In consequence we find a Cesàro-Orlicz sequence space different from c0 which has no extreme points. Some examples show that in these spaces the notion of the strong U-point is essentially stronger than the notion of the extreme point. Various examples presented in this paper show that there are some differences between criteria for extreme points and strong U-points in Orlicz spaces and in Cesàro-Orlicz spaces. We also show that the uniqueness of the local best approximation needs the notion of SU-point, that is, the notion of the extreme point is not strong enough here. 相似文献
10.
On Best Approximations from RS-sets in Complex Banach Spaces 总被引:2,自引:0,他引:2
ChongLI 《数学学报(英文版)》2005,21(1):31-38
The concept of an RS-set in a complex Banach space is introduced and the problem of best approximation from an RS-set in a complex space is investigated. Results consisting of characterizations, uniqueness and strong uniqueness are established, 相似文献
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In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some examples are given to show the results in this article are best possible. 相似文献
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Some results on the invariant regions ,existence and uniqueness of solutions to a class of integrodifferential systems are established. Applying these results to integrodifferential systems with a small parameter ε > 0, we obtain,in particular, some estimates of solutions uniform in ε > 0. 相似文献
16.
In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some examples are given to show the results in this article are best possible. 相似文献
17.
R. W. Owens 《Numerical Functional Analysis & Optimization》2013,34(4):447-455
Deutsch [4] has suggested that some problems of best simultaneous approximation might profitably be viewed as problems of best approximation in an appropriate product space. A few authors have touched upon this approach; none, however, have pursued it consistently or developed a complete problem along such a line, even in the simplest of cases. In this paper, we show that Deutsch's suggestion can easily be carried out using known results from approximation theory to establish existence, uniqueness, and characterization results. An algorithm guaranteed to converge strongly to the element of best simultaneous approximation under certain circumstances is also proposed. 相似文献
18.
We study bilateral problems for a second order parabolic operator with principal part not of divergence form. We prove existence, uniqueness, Holder-continuity and approximation results for both strong and generalized solutions. 相似文献
19.
Shigeo Tarama 《Proceedings of the American Mathematical Society》2004,132(12):3629-3639
In this paper we show the strong uniqueness for the plate equations. By using the idea due to Lebeau we transform the given operator to the elliptic operators to which we apply the Carleman estimates given by Alinhac and Lerner.
20.
Qiu-yi DAI~ 《中国科学A辑(英文版)》2007,50(8):1141-1156
This paper is devoted to the study of existence,uniqueness and non-degeneracy of positive solutions of semi-linear elliptic equations.A necessary and sufficient condition for the existence of positive solutions to problems is given.We prove that if the uniqueness and non-degeneracy results are valid for positive solutions of a class of semi-linear elliptic equations,then they are still valid when one perturbs the differential operator a little bit.As consequences,some uniqueness results of positive solutions under the domain perturbation are also obtained. 相似文献