José M. Quesada
University of Jaén
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Publication
Featured researches published by José M. Quesada.
Journal of Approximation Theory | 2012
Jorge Bustamante; José M. Quesada; Reinaldo Martínez-Cruz
We find the polynomials of the best one-sided approximation to the Heaviside and sign functions. The polynomials are obtained by Hermite interpolation at the zeros of some Jacobi polynomials. Also we give an estimate of the error of approximation and characterize the extremal points of the convex set of the best approximants.
Journal of Approximation Theory | 2006
Jorge Bustamante; José M. Quesada
In this note we present a new characterization of Bernstein operators by showing that they are the only solution of a certain extremal relation.
Journal of Approximation Theory | 2001
José M. Quesada; Juan Navas
In this paper, we consider the problem of best approximation in lp(n),1 ≤ p ≤ ∞. If hp, 1 ≤ p ≤ ∞, denotes the best lp-approximation of the element h ∈ Rn from a proper affine subspace K of Rn, h ∉ K, then limp→1 hp =h*1, where h*1 is a best l1-approximation of h from K, the so-called natural l1-approximation. Our aim is to give a complete description of the rate of convergence of hp to h*1 as p → 1.
Applied Mathematics and Computation | 2015
José A. Adell; Jorge Bustamante; José M. Quesada
We give upper and lower bounds for the moments and the uniform moments of Bernstein polynomials. Asymptotically, such bounds are best possible.
Journal of Approximation Theory | 2010
Jorge Bustamante; José M. Quesada; Lorena Morales de la Cruz
We present direct theorems for some sequences of positive linear operators in weighted spaces. The results, given in terms of some Ditzian-Totik moduli of smoothness, include estimations in norms and Becker type estimations.
Journal of Approximation Theory | 2015
Jorge Bustamante; Reinaldo Martínez-Cruz; José M. Quesada
We find the polynomials of the best one-sided approximation to a step function on - 1 , 1 . We prove that these polynomials are obtained by Hermite interpolation at the zeros of some quasi orthogonal Jacobi polynomials. We discuss the cases when there is uniqueness and, if there is not, we determine the extremal points of the convex set of the best approximants.
Journal of Approximation Theory | 2002
José M. Quesada; Juan Martínez-Moreno; Juan Navas
In this paper we consider the problem of best approximation in lpn, 1 < p ≤ ∞. If hp, 1 < p < ∞, denotes the best lp-approximation of the element h ∈ Rn from a proper affine subspace K of Rn, h ∉ K, then limp→∞hp = h*∞ where h*∞ is a best uniform approximation of h from K, the so-called strict uniform approximation. Our aim is to prove that for all r ∈ N there are αj ∈ Rn, 1 ≤ j ≤ r, such that hp = h*∞ + α1/p-1 + α2/(p-1)2 + ... + αr/(p-1)r + γpr, with γp(r) ∈ Rn and ||γp(r)|| = O(p-r-1).
Applied Mathematics Letters | 2010
Jorge Bustamante; José M. Quesada
Abstract For a function f ∈ C 2 [ 0 , 1 ] , we prove that lim t → 0 + ω φ 2 ( f , t ) t 2 = ‖ φ 2 f ″ ‖ , where ω φ 2 ( f , t ) denotes a Ditzian–Totik-type modulus of order 2. We apply this result to obtain an asymptotic property for positive linear operators related to Voronovskaja type formulae.
Approximation Theory and Its Applications | 1997
Miguel Marano; José M. Quesada
We give a construction of the maximum and the minimum of the set of nondecreasing lϕn-approximants in the discrete case, where ϕ is a positive convex function. A characterization of that set is also obtained.
Journal of Inequalities and Applications | 2018
José A. Adell; Jorge Bustamante; Juán J. Merino; José M. Quesada
We present a realization for some K-functionals associated with Jacobi expansions in terms of generalized Jacobi–Weierstrass operators. Fractional powers of the operators as well as results concerning simultaneous approximation and Nikolskii–Stechkin type inequalities are also considered.