This article is cited in 8 papers

Best Polynomial Approximations and the Widths of Function Classes in $L_{2}$

M. Sh. Shabozov^a, K. Tukhliev

^a Institute of Mathematics, Academy of Sciences of Republic of Tajikistan, Dushanbe

Abstract: Sharp Jackson–Stechkin type inequalities in which the modulus of continuity of $m$th order of functions is defined via the Steklov function are obtained. For the classes of functions defined by these moduli of continuity, exact values of various $n$-widths are derived.

Keywords: best polynomial approximation, Jackson–Stechkin type inequality, function classes in $L_{2}$.

UDC: 517.5

Received: 21.11.2011
Revised: 06.12.2012

DOI: 10.4213/mzm9306

 English version: Mathematical Notes, 2013, 94:6, 930–937

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