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 Trudy Inst. Mat. i Mekh. UrO RAN, 2019, Volume 25, Number 4, Pages 255–264 (Mi timm1691)

Sharp inequalities of Jackson-Stechkin type for periodic functions in $L_2$ differentiable in the Weyl sense

M. Sh. Shabozovab, A. A. Shabozovaab

a Tajik National University, Dushanbe
b University of Central Asia

Abstract: For periodic functions differentiable in the sense of Weyl and belonging to the space $L_{2}$, sharp inequalities of Jackson–Stechkin type are obtained for a special $m$th-order modulus of continuity generated by the Steklov operator (function). Similar characteristics of smoothness of functions were considered earlier by V. A. Abilov, F. V. Abilova, V. M. Kokilashvili, S. B. Vakarchuk, V. I. Zabutnaya, K. Tukhliev, etc. For classes of functions defined in terms of these characteristics, we solve a number of extremal problems of polynomial approximation theory.

Keywords: best approximation, periodic function, special modulus of continuity, Jackson–Stechkin inequalities, extremal problems.

DOI: https://doi.org/10.21538/0134-4889-2019-25-4-255-264

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Bibliographic databases:

UDC: 517.5
MSC: 42C10, 47A58
Revised: 31.10.2019
Accepted:11.11.2019

Citation: M. Sh. Shabozov, A. A. Shabozova, “Sharp inequalities of Jackson-Stechkin type for periodic functions in $L_2$ differentiable in the Weyl sense”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 4, 2019, 255–264

Citation in format AMSBIB
\Bibitem{ShaSha19} \by M.~Sh.~Shabozov, A.~A.~Shabozova \paper Sharp inequalities of Jackson-Stechkin type for periodic functions in $L_2$ differentiable in the Weyl sense \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2019 \vol 25 \issue 4 \pages 255--264 \mathnet{http://mi.mathnet.ru/timm1691} \crossref{https://doi.org/10.21538/0134-4889-2019-25-4-255-264} \elib{http://elibrary.ru/item.asp?id=41455542}