Approximation of Discontinuous Functions by Positive Linear Operators. A Probabilistic Approach
Adell, J.A. (Universidad de Zaragoza) ; Garrancho, P. ; Martínez-Sánchez, F.J.
Resumen: We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms of a local first modulus of continuity, are best possible, in the sense that we can construct particular sequences of operators attaining them. When applied to functions of bounded variation or absolutely continuous functions having derivatives of bounded variation, these upper bounds are better and simpler to compute than the usual total variation bounds. The particular case of the Bernstein polynomials is thoroughly discussed. We use a probabilistic approach based on representations of such operators in terms of expectations of random variables.
Idioma: Inglés
DOI: 10.1002/mma.70341
Año: 2025
Publicado en: Mathematical Methods in the Applied Sciences (2025), [14 pp.]
ISSN: 0170-4214
Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-23R
Tipo y forma: Article (Published version)
Área (Departamento): Área Estadís. Investig. Opera. (Dpto. Métodos Estadísticos)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes.
Exportado de SIDERAL (2025-12-04-14:38:54)
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Idioma: Inglés
DOI: 10.1002/mma.70341
Año: 2025
Publicado en: Mathematical Methods in the Applied Sciences (2025), [14 pp.]
ISSN: 0170-4214
Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-23R
Tipo y forma: Article (Published version)
Área (Departamento): Área Estadís. Investig. Opera. (Dpto. Métodos Estadísticos)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. Exportado de SIDERAL (2025-12-04-14:38:54)
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Articles > Artículos por área > Estadística e Investigación Operativa
Record created 2025-12-04, last modified 2025-12-04