This article is cited in 2 papers

The best one-sided approximation of the classes $W^rH_\omega$

V. G. Doronin, A. A. Ligun

Dneprodzerzhinsk Industrial Institute

Abstract: In this paper we calculate the upper bounds of the best one-sided approximations, by trigonometric polynomials and splines of minimal defect in the metric of the space $L$, of the classes $W^rH_\omega$ ($r=2,4,6,\dots$) of all $2\pi$-periodic functions $f(x)$ that are continuous together with their $r$-th derivative $f^r(x)$ and such that for any points $x'$ and $x''$ we have $|f^r(x')-f^r(x'')|\le\omega(|x'-x''|)$, where $\omega(t)$ is a modulus of continuity that is convex upwards.

Received: 16.02.1976

 English version: Mathematical Notes, 1977, 21:3, 174–182

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