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Dive into the research topics where José M. Quesada is active.

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Featured researches published by José M. Quesada.


Journal of Approximation Theory | 2012

Full length article: Best one-sided L1 approximation to the Heaviside and sign functions

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

On an extremal relation of Bernstein operators

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

Rate of Convergence of the Linear Discrete Polya Algorithm

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

Sharp upper and lower bounds for the moments of Bernstein polynomials

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

Direct estimate for positive linear operators in polynomial weighted spaces

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

Quasi orthogonal Jacobi polynomials and best one-sided L 1 approximation to step functions

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

Asymptotic behaviour of best l p -approximations from affine subspaces

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

A property of Ditzian–Totik second order moduli

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

Monotone Iϕ-approximation

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

Generalized Jacobi–Weierstrass operators and Jacobi expansions

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.

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Jorge Bustamante

Benemérita Universidad Autónoma de Puebla

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Reinaldo Martínez-Cruz

Benemérita Universidad Autónoma de Puebla

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Abisaí Carrillo-Zentella

Benemérita Universidad Autónoma de Puebla

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Lorena Morales de la Cruz

Benemérita Universidad Autónoma de Puebla

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