Abstract:
The Jackson–Stechkin inequality is considered, which estimates the value of the best uniform approximation of a continuous function by algebraic polynomials on a closed interval in terms of values of the modulus of continuity of the approximated function. A variant of the inequality with second-order modulus of continuity and explicit specification of the argument of the modulus of continuity and the constant is proved.
Keywords:
Jackson inequality, approximation by algebraic polynomials, modulus of continuity.
\Bibitem{Mir10}
\by A.~V.~Mironenko
\paper On the Jackson--Stechkin inequality for algebraic polynomials
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2010
\vol 16
\issue 4
\pages 246--253
\mathnet{http://mi.mathnet.ru/timm658}
\elib{https://elibrary.ru/item.asp?id=15318505}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2011
\vol 273
\issue , suppl. 1
\pages S116--S123
\crossref{https://doi.org/10.1134/S0081543811050129}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000305481300012}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79959233130}
Linking options:
https://www.mathnet.ru/eng/timm658
https://www.mathnet.ru/eng/timm/v16/i4/p246
This publication is cited in the following 2 articles:
A. G. Babenko, Yu. V. Kryakin, “On constants in the Jackson–Stechkin theorem in the case of approximation by algebraic polynomials”, Proc. Steklov Inst. Math., 303 (2018), 18–30
Gocheva-Ilieva S.G., Feschiev I.H., “New Recursive Representations for the Favard Constants with Application to Multiple Singular Integrals and Summation of Series”, Abstract Appl. Anal., 2013, 523618
Citation in format AMSBIB
Contact us: