The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen

Full-Text PDF (1010 KB) | Metadata | Table of Contents | ZAA summary
Volume 3, Issue 2, 1984, pp. 167–178
DOI: 10.4171/ZAA/98

Published online: 1984-04-30

Some properties of a new kind of modulus of smoothness

Vilmos Totik[1]

(1) University of Szeged, Hungary

The modulus of smoothness $$\omega (f, \delta)_{\varphi, p} = \mathrm {sup}_{0 < h ≤ \delta} \| \Delta^2_{h, \varphi} \|_{L^p}$$ has arisen during the investigation of positive operators of the Kantorovich type. Here we show that $\omega_{\varphi, p}$ resembles the ordinary case $\varphi = 1$ and we give the characterization of those functions $f$ for which $\omega (f, \delta)_{\varphi, p} = O (\delta^2)$. The results obtained have applications to positive operators.

No keywords available for this article.

Totik Vilmos: Some properties of a new kind of modulus of smoothness. Z. Anal. Anwend. 3 (1984), 167-178. doi: 10.4171/ZAA/98