DM-Artículos
URI permanente para esta colecciónhttps://hdl.handle.net/10953/255
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Examinando DM-Artículos por Autor "Cárdenas-Morales, Daniel"
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Ítem Approximation rate and saturation under generalized convergence(American Institute of Mathematical Sciences, 2024-02) Garrancho, Pedro; Martínez-Sánchez, Francisco-Javier; Cárdenas-Morales, DanielIn this paper we prove a quantitative result about the convergence of sequences of functions de ned from linear operators. The notion of conver- gence used here is the one given in [8]. The operators will be assumed to satisfy a shape preserving property associated with certain generalized deriv- ative. We also study the saturation class, from the asymptotic condition that the sequence of operators ful lls. Finally, as applications, we show how the notion of weighted g-statistical convergence, recently studied by A. Adem and M. Altinok [3], can be moved to the setting of approximation theory. Besides, we give a non standard example that shows the applicability of the results.Ítem Asymptotic and Non-asymptotic Results in the Approximation by Bernstein Polynomials(Birkhäuser - Springer, 2022-06-29) Adell, José A.; Cárdenas-Morales, DanielThis paper deals with the approximation of functions by the classical Bernstein polynomials in terms of the Ditzian–Totik modulus of smoothness. Asymptotic and non-asymptotic results are respectively stated for continuous and twice continuously differentiable functions. By using a probabilistic approach, known results are either completed or strengthened.Ítem Estimates in direct inequalities for the Szász–Mirakyan operator(Springer, 2022-12-16) Adell, José A.; Cárdenas-Morales, DanielThis paper deals with the approximation of continuous functions by the classical Szász– Mirakyan operator. We give new bounds for the constant in front of the second order Ditzian–Totik modulus of smoothness in direct inequalities. Asymptotic and non asymptotic results are stated. We use both analytical and probabilistic methods, the latter involving the representation of the operators in terms of the standard Poisson process. A smoothing technique based on a modification of the Steklov means is also applied.Ítem On the rates of pointwise convergence for Bernstein polynomials(Birkhäuser, 2025) Adell, José Antonio; Cárdenas-Morales, Daniel; López-Moreno, Antonio JesúsLet f be a real bounded function defined on the interval [0, 1], which is affine on a subinterval (a,b) of [0,1], and let Bnf be its associated nth Bernstein polynomial. We prove that, for any x in (a,b), |Bnf(x)-f(x)| converges to 0 as n tends to infinity at an exponential rate of decay. Moreover, we show that this property is no longer true at the boundary of (a, b). For Bernstein–Kantorovich type operators similar properties hold, whenever f is assumed to be constant instead of affine.Ítem On the uniqueness conjecture for the maximum Stirling numbers of the second kind(Springer, 2021-04-15) Adell, José A.; Cárdenas-Morales, DanielThe Stirling numbers of the second kind S(n,k) satisfy S(n,0) < · · · < S(n,kn) ≥ S(n,kn+1) > · · · > S(n,n). A long standing conjecture asserts that there exists no n ≥ 3 such that S(n,kn) = S(n,kn +1). In this note, we give a characterization of this conjecture in terms of multinomial probabilities, as well as sufficient conditions on n ensuring that S(n,kn)> S(n,kn+1).Ítem Random Linear Operators Arising from Piecewise Linear Interpolation on the Unit Interval(Birkhäuser - Springer, 2022-09-09) Adell, José A.; Cárdenas-Morales, DanielWe introduce a sequence of random linear operators arising from piecewise linear interpolation at a set of random nodes on the unit interval. We show that such operators uniformly converge in probability to the target function, providing at the same time rates of convergence. Analogous results are shown for their deterministic counterparts, derived by taking expectations of the aforementioned random operators. Special attention is paid to the case in which the random nodes are the uniform order statistics, where an explicit form for their associated deterministic operators is provided. This allows us to compare the speed of convergence of the aforementioned operators with that of the random and deterministic Bernstein polynomialsÍtem Stochastic Bernstein polynomials: uniform convergence in probability with rates(Springer, 2020-02-27) Adell, José A.; Cárdenas-Morales, DanielWe introduce stochastic variants of the classical Bernstein polynomials associated with a continuous function f , built up from a general triangular array of random variables. We discuss the uniform convergence in probability of the approximation process that they represent, providing at the same time rates of convergence. In the particular case in which the triangular array of random variables consists of the uniform order statistics, we give a positive answer to a conjectured raised in Wu and Zhou (Adv. Comput. Math. 46, 8, 2020) about an exponential rate of convergence in probability.