S. B. Vakarchuk, V. I. Zabutnaya, “A Sharp Inequality of Jackson–Stechkin type in <nobr>$L_2$</nobr> and the Widths of Functional Classes”, Mat. Zametki, 2009, Volume 86, Issue 3,Pages <nobr>328

This article is cited in 29 papers

A Sharp Inequality of Jackson–Stechkin type in $L_2$ and the Widths of Functional Classes

S. B. Vakarchuk^a, V. I. Zabutnaya^b

^a Dnepropetrovsk University of Economics and Law
^b Dnepropetrovsk National University

Abstract: We obtain sharp inequalities of Jackson–Stechkin type in which the modulus of continuity of the function is defined in terms of the Steklov function. For classes of functions given by this characteristic, we obtain sharp values of the $n$-widths.

Keywords: inequality of Jackson–Stechkin type, modulus of continuity, Fourier series, Steklov function, Bernstein $n$-width, Kolmogorov $n$-width, Gelfand $n$-width.

UDC: 517.5

Received: 18.06.2007

DOI: 10.4213/mzm3901