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- Fernando Mazzone, Héctor Cuenya
- Journal of Approximation Theory
- 2001

- Héctor H Cuenya, Fabián E Levis, Claudia V Ridolfi
- 2012

The space L with this norm is a Banach space (see [1]). If E ∈ B and μ(E) > 0, then ∥ · ∥j,E is a seminorm on L(X). In the particular case, j (t) = t, we will use the notation ∥ · ∥p,E instead of ∥ · ∥j,E. Let N ⊂ M , N Î N, be the class of all algebraic polynomials of degree at most N, with real coefficients. Given E ∈ B , we recall that a polynomial gE Î… (More)

- Héctor Cuenya, Fabián E. Levis
- Journal of Approximation Theory
- 2010

- Fernando Mazzone, Héctor Cuenya
- Journal of Approximation Theory
- 2002

Let ðO;A; P Þ be a measurable space and L A a sub-s-lattice of the s-algebra A: For X 2 L1ðO;A; P Þ we denote by PLX the set of conditional 1-mean (or best approximants) of X given L1ðLÞ (the set of all L-measurable and integrable functions). In this paper, we obtain characterizations of the elements in PLX ; similar to those obtained by Landers and Rogge… (More)

- H. H. CUENYA, F. E. LEVIS
- 2016

We study the behavior of best simultaneous (lq , Lp)-approximation by rational functions on an interval, when the measure tends to zero. In addition, we consider the case of polynomial approximation on a finite union of intervals. We also get an interpolation result.

In this paper we give sufficient conditions over the differentiability of a function to assure existence of the best local approximant in Lp-spaces, 0 < p ≤ ∞. These conditions are weaker than those given in previous papers. For p = 2 we show that, in a certain way, they are also necessary. In addition, we characterize the best local approximant.

- Fabián E. Levis, Héctor Cuenya
- Journal of Approximation Theory
- 2004

Given f E L2(lR n), E > 0 and x E IR n we consider P(t) to be the polynomial of best approximation to f in the L2-norm by elements of IIm over the set x + EC, where C denote a suitable parallelepiped. Let T;'f(x) be the Qth-coefficient of P when it has been developed in the base {t"'/Q!}. In this paper we show that the operator T;' is a composition of a… (More)

In this paper, we prove existence of optimal bundles for a countable set of data in a broad class of normed spaces, which extend previous known results for a finite data set in a Hilbert space. In addition, we study the behavior of deviations and diameters for an increasing sequence of data sets.

- F. E. LEVIS, H. H. CUENYA
- 2004

Let (Ω,A, μ) be a σ-finite nonatomic measure space and let Λw,φ be the Orlicz-Lorentz space. We study the Gateaux differentiability of the functional Ψw,φ(f) = ∞ ∫ 0 φ(f∗)w. More precisely we give an exact characterization of those points in the Orlicz-Lorentz space Λw,φ where the Gateaux derivative exists. This paper extends known results already on Lorent… (More)

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