This article is cited in 1 paper

The best one-sided approximation of one class of functions by another

V. G. Doronin, A. A. Ligun

Dnepropetrovsk State University

Abstract: We concern ourselves with problems of the best one-sided approximation of classes of continuous functions. We obtain estimates of the best one-sided approximation of one class of functions by another, and we find exact values of the upper bounds of the best one-sided approximations on the classes $H_\omega$ of $2\pi$-periodic functions [given by an arbitrary convex modulus of continuity $\omega(t)$] by trigonometric polynomials of order not higher than $n-1$ in the $L_{2\pi}$ metric.

UDC: 517.5

Received: 12.03.1973

 English version: Mathematical Notes, 1973, 14:5, 919–922

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