Towards the best constant in front of the Ditzian-Totik modulus of smoothness

Adell, J.A. (Universidad de Zaragoza) ; Lekuona, A. (Universidad de Zaragoza)

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

Factor impacto JCR: 0.791 (2016)

Categ. JCR: MATHEMATICS rank: 106 / 310 = 0.342 (2016) - Q2 - T2
Categ. JCR: MATHEMATICS, APPLIED rank: 157 / 255 = 0.616 (2016) - Q3 - T2

Factor impacto SCIMAGO: 0.807 - Analysis (Q2) - Discrete Mathematics and Combinatorics (Q2) - Applied Mathematics (Q2)

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): Área Estadís. Investig. Opera. (Dpto. Métodos Estadísticos)