Functiones et Approximatio Commentarii Mathematici

On the Riemann integrability of the $n$-th local modulus of continuity

Steffen J. Goebbels

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Abstract

The present note proves Riemann integrability of the $n$-th local modulus of continuity which is used within the definition of averaged moduli of smoothness ($\tau$-moduli). In addition it is shown that an averaged supremum norm ($\delta$-norm) can be calculated using the Riemann integral.

Article information

Source
Funct. Approx. Comment. Math., Volume 34 (2005), 7-17.

Dates
First available in Project Euclid: 29 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.facm/1538186583

Digital Object Identifier
doi:10.7169/facm/1538186583

Mathematical Reviews number (MathSciNet)
MR2269660

Zentralblatt MATH identifier
1123.26008

Subjects
Primary: 26A42: Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX]
Secondary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27} 41A25: Rate of convergence, degree of approximation 41A99: None of the above, but in this section

Keywords
averaged modulus of smoothness local modulus of continuity Riemann integrability

Citation

Goebbels, Steffen J. On the Riemann integrability of the $n$-th local modulus of continuity. Funct. Approx. Comment. Math. 34 (2005), 7--17. doi:10.7169/facm/1538186583. https://projecteuclid.org/euclid.facm/1538186583


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