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Resumen: We give accurate estimates for the constants (Formula presented.), where I = R or I = 0, 8), Ln is a positive linear operator acting on real functions f defined on the interval I, A(I) is a certain subset of such function, and ¿s 2(f; ·) is the Ditzian-Totik modulus of smoothness of f with weight function s. This is done under the assumption that s is concave and satisfies some simple boundary conditions at the endpoint of I, if any. Two illustrative examples closely connected are discussed, namely, Weierstrass and Szàsz-Mirakyan operators. In the first case, which involves the usual second modulus, we obtain the exact constants when A(R) is the set of convex functions or a suitable set of continuous piecewise linear functions.
Idioma: Inglés
DOI: 10.1186/s13660-016-1078-0
Año: 2016
Publicado en: JOURNAL OF INEQUALITIES AND APPLICATIONS 2016, 137 (2016), [17 pp.]
ISSN: 1025-5834
Financiación: info:eu-repo/grantAgreement/ES/DGA/E64
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2015-67006-P
Tipo y forma: Article (Published version)
Área (Departamento): Estadística e Investigación Operativa (Departamento de Métodos Estadísticos)

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