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1.
强CHIP性质和广义限制域逼近的特征   总被引:4,自引:0,他引:4  
方东辉  李冲  杨文善 《数学学报》2004,47(6):1115-112
本文研究了广义限制域的最佳逼近问题,在允许有有限个节点的情况下,引入次强内点条件的概念,并将优化理论中的强CHIP性质等概念应用到本文所研究的问题中,刻画了次强内点、强CHIP性质和最佳逼近的特征之间的关系.作为推论,我们得到了广义限制最佳逼近的Kolmogorov型和“零属于凸包”型等特征定理.  相似文献   

2.
双连续n次积分C余弦函数的逼近定理   总被引:4,自引:0,他引:4  
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.  相似文献   

3.
设X是一致凸空间,G为X中太阳集,R.Smarzewski[1]证明了g∈G对x∈的最佳逼近具有广义强唯一性,本文讨论其逆,在最佳逼近是广义强唯一的条件下,研究了空间的凸性和逼近集的太阳性.  相似文献   

4.
徐士英 《数学杂志》1996,16(3):321-328
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.
文中证明了核邻型的光滑条件分位过程的强逼近,获得了其一致逼近速度.并由此结果推导出了光滑条件分位估计的渐近正态性、弱收敛和对数律等深刻结果.  相似文献   

6.
霍永亮  刘三阳 《应用数学》2008,21(2):322-325
本文提出强上图收敛的概念,讨论了逼近随机规划的目标函数序列的强上图收敛性,研究了逼近随机规划最优值和最优解集的收敛性条件,得到了一类随机规划逼近最优值和最优解集的收敛性.  相似文献   

7.
条件t-分位数核估计的逼近速度   总被引:1,自引:0,他引:1       下载免费PDF全文
该文研究了条件狋 分位数核估计的逼近速度问题.在适当的条件下,给出了核估计的强收敛速度、正态逼近速度和Bootstrap逼近速度.  相似文献   

8.
研究了有界线性算子空间中最佳逼近的强惟一性问题,给出了线性和非线性最佳逼近的强惟一性定理。  相似文献   

9.
王廷辅  任重道 《数学杂志》1993,13(4):443-452
一致凸点(UR点)和弱一致凸点(WUR点)是Banach空间几何学的重要概念,它们在逼近轮,控制论,变分不等式等分支中都有广泛的应用。本文给出了在Orlicz空间中一致凸点(UR点)和弱一致凸点(WUR点)的判别准则,据此方便地得到了Orlicz空间是局部一致凸、弱局部一致凸的条件。  相似文献   

10.
Banach空间中同时逼近问题的适定性   总被引:1,自引:0,他引:1       下载免费PDF全文
研究一般Banach空间X中同时逼近问题的适定性.对严格凸的KadecBanach空间X中的相对有界弱紧闭子集G,建立了关于最佳同时逼近问题适定Bair纲结果.进一步,当X是一致凸空间时,证明了E(G)中使其最佳同时逼近问题不适定的序列在E(G)中是一个σ-多孔集.另外,还研究了关于最佳同时逼近元具有分歧域的集合G的几乎性.  相似文献   

11.
The BCQ and the Abadie CQ for infinite systems of convex inequalities in Banach spaces are characterized in terms of the upper semi-continuity of the convex cones generated by the subdifferentials of active convex functions. Some relationships with other constraint qualifications such as the CPLV and the Slate condition are also studied. Applications in best approximation theory are provided.  相似文献   

12.
凌博  刘永平 《数学学报》2017,60(3):389-400
我们研究了由仅有实零点的代数多项式导出的微分算子确定的广义Sobolev类利用指数型整函数作为逼近工具的最佳限制逼近问题.利用Fourier变换和周期化等方法,得到在L_2(R)范数下的广义Sobolev光滑函数类的相对平均宽度和最佳限制逼近的精确常数,以及当0是这个代数多项式的一个至多2重的零点时,得到最佳限制逼近在L_1(R)范数和一致范数下的广义Sobolev类的精确到阶的结果.  相似文献   

13.
In this study, we propose a 3D generalized micro heat transfer model in an N-carrier system with the Neumann boundary condition in spherical coordinates, which can be applied to describe the non-equilibrium heating in biological cells. Two improved unconditionally stable Crank-Nicholson schemes are then presented for solving the generalized model. In particular, we delicately adjust the location of the interior grid point that is next to the boundary so that the Neumann boundary condition can be applied directly without discretization. As such, a second-order accurate finite difference scheme without using any fictitious grid points is obtained. The convergence rates of the numerical solution are tested by an example. Results show that the convergence rates of the present schemes are about 2.0 with respect to the spatial variable r, which improves the accuracy of the Crank-Nicholson scheme coupled with the conventional first-order approximation for the Neumann boundary condition.  相似文献   

14.
1PreliminariesandExistenceForfEC[0,1],A.PinkusandO.Shi.h.[l]introducedthefollowingmeasures,'Thesupremaareattainable,andqE[1,co)Inthecaseq=1,wesimplyletWiththismeasurestA.PinkusandO.ShishahavestudiedbestapproximationbyalgebraicpolynondaISofdegree5n.Later,MaandShi[2]11avestudiedthecaseofbestapproximationfromratiollalpolyllollilalsR:,usingthesamegaugeill'JI1.TheyallgetthesimilarresultsforChebyshevapproximation,includingalternatiolltheoremascharacterisatiollforthebestappro~swhichisthegeom…  相似文献   

15.
In this paper, based on basic constraint qualification (BCQ) and strong BCQ for convex generalized equation, we are inspired to further discuss constraint qualifications of BCQ and strong BCQ for nonconvex generalized equation and then establish their various characterizations. As applications, we use these constraint qualifications to study metric subregularity of nonconvex generalized equation and provide necessary and/or sufficient conditions in terms of constraint qualifications considered herein to ensure nonconvex generalized equation having metric subregularity.  相似文献   

16.
The operator of best uniform approximation of real, continuous functions by elements of a finite space is considered. It is shown that the Lipschitz condition for the operator of best approximation by generalized polynomials is satisfied for each function having a characteristic set of maximal dimension.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 17–19, 1987.  相似文献   

17.
The problem of best uniform approximation by polynomials with restricted ranges of some of their derivatives to functions not satisfying the same restrictions is treated. Results concerning the number of alternations of the best approximating polynomial are derived, and the impossibility of approximating arbitrarily closely functions with one derivative outside the range is proved.  相似文献   

18.
Mathematical programming problems with unattained infima or unbounded optimal solution sets are dual to problems which lackinterior points, e.g., problems for which the Slater condition fails to hold or for which the hypothesis of Fenchel's theorem fails to hold. In such cases, it is possible to project the unbounded problem onto a subspace and to restrict the dual problem to an affine set so that the infima are not altered. After a finite sequence of such projections and restrictions, dual problems are obtained which have bounded optimal solution sets andinterior points. Although results of this kind have occasionally been used in other contexts, it is in geometric programming (both in the original psynomial form and the generalized form) where such methods appear most useful. In this paper, we present a treatment of dual projection and restriction methods developed in terms of dual generalized geometric programming problems. Analogous results are given for Fenchel and ordinary dual problems.This research was supported in part by Grant No. AFOSR-73-2516 from the Air Force Office of Scientific Research and by Grant No. NSF-ENG-76-10260 from the National Science Foundation.The authors wish to express their appreciation to the referees for several helpful comments.  相似文献   

19.
The existence of saddle point of the Lagrange function for a convex programming problem in Banach spaces ordered by a cone with empty interior is established under a strong simultaneity condition. As a consequence, the Kuhn–Tucker conditions are derived. It is shown that the Slater and the strong simultaneity condition are equivalent if the cone determining the partial order has an interior.  相似文献   

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