Abstract
The precise value is given of the upper bound of the deviation in the Lp metric (1 < p < ∞) of a function f(x) in the class H ω , given by a convex modulus of continuityω(t), from its polygonal approximation at the points xk=k/n (k=0, 1 ...,n).
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V. N. Malozemov, “The deviation of polygonal functions,” Vestnik. Leningr. Univ., No. 7, 150–153 (1966).
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Translated from Matematicheskie Zametki, Vol. 5, No. 1, pp. 31–37, 1969.
I would like to express my appreciation to A. A. Nudel'man for suggesting the problem considered here and for his help.
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Storchai, V.F. The deviation of polygonal functions in the Lp metric. Mathematical Notes of the Academy of Sciences of the USSR 5, 21–25 (1969). https://doi.org/10.1007/BF01098710
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DOI: https://doi.org/10.1007/BF01098710