Results 1 to 10 of about 109,893 (171)
Uniqueness of best approximation by monotone polynomials
Journal of Approximation Theory, 1971 The purpose of this paper is twofold. First, we prove the uniqueness of a polynomial of best uniform approximation, in a certain class P of “monotone” polynomials, to a given continuous function. This is the content of Theorem 3.1 which complements the results of Lorentz and Zeller [l].
R. Lorentz
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Uniqueness of Hahn-Banach extensions and unique best approximation. [PDF]
Transactions of the American Mathematical Society, 1960 Introduction. The Hahn-Banach theorem states that a linear functional defined on a subspace M of a normed linear space E has at least one extension (with the same norm) to the whole of E. We intend to investigate those subspaces M for which this extension is unique, that is, those subspaces M having property U: Each linear functional on M has a unique ...
R. Phelps
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Uniqueness of Best Approximation with Coefficient Constraints
Rocky Mountain Journal of Mathematics, 1993 Let for given \(\alpha= (\alpha_ 1,\dots, \alpha_ n)\) and \(\beta= (\beta_ 1,\dots, \beta_ n)\), with \(-\infty\leq \alpha_ i< \beta_ i\leq\infty\), \(i=1,\dots, n\), and continuous functions \(u_ 1,\dots,u_ n\), set \(U(\alpha,\beta)= \{\sum_{i=1}^ n a_ i U_ i\); \(\alpha_ i\leq a_ i\leq\beta_ i\), \(i=1,\dots, n\}\). In this paper the conditions for
Chengmin Yang
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Existence, uniqueness, and stability of best and near-best approximations
Russian Mathematical Surveys, 2023 Existence and stability of $\varepsilon$-selections (selections of operators of near-best approximation) are studied. Results relating the existence of continuous $\varepsilon$-selections with other approximative and structural properties of approximating sets are given.
Alimov, Alexey R. +2 more
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Journal of Numerical Analysis and Approximation Theory, 2003 A well known result of R. R. Phelps (1960) asserts that in order that every linear continuous functional, defined on a subspace \(Y\) of a real normed space \(X\), have a unique norm preserving extension it is necessary and sufficient that its ...
Costică Mustăţa
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Uniqueness of a simple partial fraction of best approximation
Journal of Mathematical Sciences, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M. Komarov
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Uniqueness of best simultaneous approximation and strictly interpolating subspaces
Journal of Approximation Theory, 1984 If F,G are subsets of a normed linear space E,F bounded, a best simultaneous approximation to F in G is \(y_ 0\in G\) minimizing \(r(y,G)=\sup_{x\in F}\| x-y\|\). The set of best simultaneous approximations to F in G is denoted \(Z_ G(F)\) and called also the ''Chebyshev center'' for F in G, and \(r_ G(F)=\inf_{y\in G}r(y,F)\) is called the ''Chebyshev
D. Amir
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Polynomials with positive coefficients: Uniqueness of best approximation
Journal of Approximation Theory, 1977 E. Passow
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Uniqueness of best Chebyshev approximation on subsets
Journal of Approximation Theory, 1975 C. Dunham
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Uniqueness of best approximation of a function and its derivatives
Journal of Approximation Theory, 1973 B. Chalmers
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