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On the Uniqueness of p-Best Approximation in Probabilistic Normed Spaces
International Journal of Nonlinear Sciences and Numerical Simulation, 2017Abstract The main aim of this paper is to present some basic as well as essential results involving the notion of p-Chebyshev sets in probabilistic normed spaces. In particular, we discuss the convexity of p-Chebyshev sets, decomposition of the space into its special subspaces, and we see a characterization of p-Chebyshev sets in ...
H. Goudarzi
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Strong uniqueness of generalized polynomial of best approximation having bounded coefficients
Acta Mathematicae Applicatae Sinica, 1991zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xu Shusheng
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UNIQUENESS OF BEST φ–APPROXIMATION BY 3-CONVEX FUNCTIONS
Numerical Functional Analysis and Optimization, 2001We prove the uniqueness of best 3-convex φ-approximation to a continuous function f ∈ L φ (J 0), where J 0 is a bounded, open interval and φ : [0, + ∞) → [0, + ∞) is a convex function that generalizes the p th–power functions, p ≥ 1.
A. Damas, M. Marano
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Uniqueness of the polynomial of best L-approximation of discontinuous functions
Mathematical Notes, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
N. K. Rakhmetov
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Uniqueness of best α-norm approximation andA-spaces
Numerical Functional Analysis and Optimization, 1992Let ...
Chengmin Yang
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Ukrainian Mathematical Journal, 1994
For the real function \(f\) defined on \(I = [a,b]\) let \(|f |_{\alpha, \beta}\) be given by \(|f |_{\alpha, \beta} = \alpha f_+ + \beta f_-\) where \(f_\pm (x) = \max \{\pm f(x), 0\}\). When \(f \in L_1 (I)\) the authors consider the norm of \(f\) defined by \[ |f |_{1; \alpha \beta} = \int_I \bigl |f(x) \bigr |_{\alpha, \beta} dx. \] For \(f \in L_1(
Babenko, V. F., Glushko, V. N.
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For the real function \(f\) defined on \(I = [a,b]\) let \(|f |_{\alpha, \beta}\) be given by \(|f |_{\alpha, \beta} = \alpha f_+ + \beta f_-\) where \(f_\pm (x) = \max \{\pm f(x), 0\}\). When \(f \in L_1 (I)\) the authors consider the norm of \(f\) defined by \[ |f |_{1; \alpha \beta} = \int_I \bigl |f(x) \bigr |_{\alpha, \beta} dx. \] For \(f \in L_1(
Babenko, V. F., Glushko, V. N.
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Uniqueness of generalized elements of best approximation
Mathematical Notes of the Academy of Sciences of the USSR, 1979L. P. Vlasov
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Uniqueness of the best approximation in mean of vector-valued functions
Mathematical Notes of the Academy of Sciences of the USSR, 1986The problem of uniqueness of an element of best mean approximation of continuous vector-valued functions is studied. The main result of this paper consists in the generalization of Jackson's theorem about uniqueness of best mean approximation in the case of convex Banach space.
A. Garkavi
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Uniqueness of best Chebyshev approximation to nearby functions
Periodica Mathematica Hungarica, 1974C. Dunham
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Existence and uniqueness of rational functions of best approximation
1935J. Walsh
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