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Zeitschrift für Analysis und ihre Anwendungen


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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.

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