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best approximation BY DOWNWARD SETS WITH APPLICATIONS

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Analysis in Theory and Applications 2006年第1期22卷 20-40页

作者： H.Mohebi A.M.Rubinov Shahid Bahonar University of Kerman Iran University of Ballarat Australia

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X

关键词： best approximation downward set proximinal set Chebyshev set Banach lattice

Monotonicity and best approximation in Banach Lattices

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Acta Mathematica Sinica,English Series 2009年第5期25卷 785-794页

作者： Shu Tao CHEN Xin HE H. HUDZIK Department of Mathematics Harbin Normal University Harbin 150080 P. R. China Faculty of Mathematics and Computer Science Adam Mickiewicz University Umultowska 87 61-614 Poznan Poland

Hudzik and Kurc discussed some best approximation problems in Banach lattices by means of monotonicities. This paper deals with more general best approximation problems in Banach lattices. Existence, uniqueness, stabi... 详细信息

关键词： Banach lattice uniform monotonicity strict monotonicity upper (lower) locally uniform monotonicity best approximation

Leibniz seminorms and best approximation from C*-subalgebras

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Science China Mathematics 2011年第11期54卷 2259-2274页

作者： RIEFFEL Marc A Department of Mathematics University of CaliforniaBerkeleyCA 94720-3840USA

We show that if B is a C*-subalgebra of a C*-algebra A such that B contains a bounded approximate identity for A,and if L is the pull-back to A of the quotient norm on A/B,then L is strongly *** connection with this situation we study certain aspects of best approximation of elements of a unital C*-algebra by elements of a unital C*-subalgebra.

关键词： C^*-subalgebras best approximation distance formula Leibniz inequality strongly-Leibniz minimal elements

ON M-IDEALS AND best approximation

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Acta Mathematicae Applicatae Sinica 1994年第2期10卷 213-219页

作者：韩德广 1. Department of Mathematics Qufu Normal University 273165 Qufu China

In this paper we will prove some theorems on the M-ideals of compact operators and the best approximation of quasitriangular operator algebras. These results improve and extend the known results in [4, 5, 7].

关键词： M-ideal best approximation compact operator.

SOME GENERALIZATIONS OF KY FAN'S best approximation THEOREM

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Analysis in Theory and Applications 2004年第2期20卷 189-198页

作者： A.R.Khan N.Hussain A.B.Thaheem King Fahd University of Petroleum and Minerals Saudi ArabiaBahauddin Zakaria University PakistanKind Fahd University of Petroleum and Minerals Saudi Arabia

We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map on metrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derived for the map stud... 详细信息

关键词： best approximation fixed point * -nonexpansive multivalued map almost quasi-convex function metrizable topological vector space hyperconvex space

best approximation BY NORMAL MATRICES WITH SPECTRAL CONSTRAINTS

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Transactions of Nanjing University of Aeronautics and Astronautics 1998年第2期15卷 88-92页

作者：戴华南京航空航天大学理学院

The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability of the problem is given. A numerical algorithm for solving the problem is provided and a numerical example is presented.

关键词： normal matrices best approximation eigenvalues inverse problems spectral constraint

A Class of Iteration Method for the best approximation Problems

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Advances in Manufacturing 1998年第1期 18-24页

作者： Wang Deren Zhao Fengguang (College of Sciences)

We propose a class of iteration methods searching the best approximately generalized polynomial, which has parallel computational function and converges to the exact solution quadratically. We first transform it into a special system of nonlinear equations with constraint, then by using to certain iteration method, we combine the two basic processes of the Remes method into a whole such that the iterative process of the system of nonlinear equations and the computation of the solution to the system of linear equations proceed alternately. A lot of numerical examples show that this method not only has good convergence property but also always converges to the exact solution of the problem accurately and rapidly for almost all initial approximations .

关键词： best approximation Chebyshev alternating point set Remes method

best constants of harmonic approximation of some convolution classes associated with Laplace operator in d-variables

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Science China Mathematics 2013年第2期56卷 301-313页

作者： LING Bo LIU YongPing School of Mathematical Sciences Beijing Normal UniversityLaboratory of Mathematics and Complex SystemsMinistry of Education

In this paper,we consider the best EFET(entire functions of the exponential type) approximations of some convolution classes associated with Laplace operator on R d and obtain exact constants in the spaces L1(R2) and ... 详细信息

关键词： best approximation exact constant Laplace operator trigonometric polynomials entire functionsof exponential type

On best approximations from RS-sets in Complex Banach Spaces

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Acta Mathematica Sinica,English Series 2005年第1期21卷 31-38页

作者： ChongLI DepartmentofMathematics ZhejiangUniversityHangzhou310027P.R.China

The concept of an RS–set in a complex Banach space is introduced and theproblem of best approximation from an RS–set in a complex space is investigated. Results consistingof characterizations, uniqueness and strong ... 详细信息

关键词： Complex RS–set best approximation Uniqueness Strong uniqueness