## Functiones et Approximatio Commentarii Mathematici

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

Steffen J. Goebbels

#### 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

#### 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