Geodesic
The deviation of polygonal functions in the $L_p$ metric
Matematičeskie zametki, Tome 5 (1969) no. 1, pp. 31-37.

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The precise value is given of the upper bound of the deviation in the $L_p$ metric $(1\le p\infty)$ of a function $f(x)$ in the class $H_\omega$, given by a convex modulus of continuity $\omega(t)$, from its polygonal approximation at the points $x_k=k/n$ ($k=0,1,\dots,n$). 
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     author = {V. F. Storchai},
     title = {The deviation of polygonal functions in the $L_p$ metric},
     journal = {Matemati\v{c}eskie zametki},
     pages = {31--37},
     publisher = {mathdoc},
     volume = {5},
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     year = {1969},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_1_a3/}
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V. F. Storchai. The deviation of polygonal functions in the $L_p$ metric. Matematičeskie zametki, Tome 5 (1969) no. 1, pp. 31-37. http://geodesic.mathdoc.fr/item/MZM_1969_5_1_a3/