Departamento de Matemáticas
URI permanente para esta comunidadhttps://hdl.handle.net/10953/44
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Examinando Departamento de Matemáticas por Materia "Ditzian–Totik modulus of smoothness"
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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 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 polynomials