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Let $D$ be a nonempty compact subset of a Banach space $X$ and denote by $S (X)$ the family of all nonempty bounded closed convex subsets of $X$ . We endow $S (X)$ with the Hausdorff metric and show that there exists a set $ℱ \subset S (X)$ such that its complement $S (X) ∖ ℱ$ is $σ$ -porous and such that for each $A \in ℱ$ and each $\tilde{x} \in D$ , the set of solutions of the best approximation problem $∥ \tilde{x} - z ∥ \to min$ , $z \in A$ , is nonempty and compact, and each minimizing sequence has a convergent subsequence.

Best approximations, fixed points and parametric projections

Tiziana Cardinali (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

If f is a continuous seminorm, we prove two f-best approximation theorems for functions Φ not necessarily continuous as a consequence of our version of Glebov's fixed point theorem. Moreover, we obtain another fixed point theorem that improves a recent result of [4]. In the last section, we study continuity-type properties of set valued parametric projections and our results improve recent theorems due to Mabizela [11].

Best approximations for the Laguerre-type Weierstrass transform on $[0, \infty [\times ℝ$ .

Jebbari, E., Soltani, F. (2005)

International Journal of Mathematics and Mathematical Sciences

Best approximations theorem for a couple in cone Banach space.

Karapınar, Erdal, Türkoğlu, Duran (2010)

Fixed Point Theory and Applications [electronic only]

Best coapproximation in metric spaces.

Narang, T.D. (1992)

Publications de l'Institut Mathématique. Nouvelle Série

Best Coapproximation in Normed Linear Spaces.

Ivan Singer, Pier L. Papini (1979)

Monatshefte für Mathematik

Best Constants Occuring with the Modulus of Continuity in the Error Estimate for Spline Interpolants of Odd Degree on Equidistant Grids.

M. Reimer (1984)

Numerische Mathematik

Best Discrete Mean Rational Approximation.

Charles B. Dunham (1974)

Aequationes mathematicae

Best N-term approximation in electronic structure calculations I. One-electron reduced density matrix

Heinz-Jürgen Flad, Wolfgang Hackbusch, Reinhold Schneider (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

We discuss best N-term approximation spaces for one-electron wavefunctions $φ_{i}$ and reduced density matrices ρ emerging from Hartree-Fock and density functional theory. The approximation spaces $A_{q}^{α} (H^{1})$ for anisotropic wavelet tensor product bases have been recently characterized by Nitsche in terms of tensor product Besov spaces. We have used the norm equivalence of these spaces to weighted $ℓ_{q}$ spaces of wavelet coefficients to proof that both $φ_{i}$ and ρ are in $A_{q}^{α} (H^{1})$ for all $α > 0$ with $α = \frac{1}{q} - \frac{1}{2}$ . Our proof is based on the...

Best N-term approximation in electronic structure calculations. II. Jastrow factors

Heinz-Jürgen Flad, Wolfgang Hackbusch, Reinhold Schneider (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a novel application of best N-term approximation theory in the framework of electronic structure calculations. The paper focusses on the description of electron correlations within a Jastrow-type ansatz for the wavefunction. As a starting point we discuss certain natural assumptions on the asymptotic behaviour of two-particle correlation functions $ℱ^{(2)}$ near electron-electron and electron-nuclear cusps. Based on Nitsche's characterization of best N-term approximation spaces $A_{q}^{α} (H^{1})$ , we prove...

In this paper we study simultaneous approximation of $n$ real-valued functions in $L_{p} [a, b]$ and give a generalization of some related results.

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Best approximation in Orlicz spaces.

Best approximation in spaces of bounded linear operators [Book]

Best Approximation in the Space of Bounded Operators and its Applications.

Best Approximation In Vector Valued Function Spaces.

Best Approximation with Exponential Orders and Intermediate Spaces.

Best approximations and porous sets

Best approximations, fixed points and parametric projections

Best approximations for the Laguerre-type Weierstrass transform on $[0, \infty [\times ℝ$ .

Best approximations theorem for a couple in cone Banach space.

Best coapproximation in metric spaces.

Best Coapproximation in Normed Linear Spaces.

Best Constants Occuring with the Modulus of Continuity in the Error Estimate for Spline Interpolants of Odd Degree on Equidistant Grids.

Best Discrete Mean Rational Approximation.

Best N-term approximation in electronic structure calculations I. One-electron reduced density matrix

Best N-term approximation in electronic structure calculations. II. Jastrow factors

Best proximity point theorems for $p$ -cyclic Meir–Keeler contractions.

Best quadrature formula for a certain class of analytic functions

Best simultaneous approximation in Orlicz spaces.

Best Simultaneous Approximation of Bounded Functions with Values in Certain Banach Spaces.

Best simultaneous $L_{p}$ approximations

Currently displaying 41 – 60 of 84