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Matematicheskie Zametki, 2021, Volume 110, Issue 3, Pages 450–458
DOI: https://doi.org/10.4213/mzm13005
(Mi mzm13005)
 

This article is cited in 1 scientific paper (total in 1 paper)

Inequalities between Best Polynomial Approximants and Smoothness Characteristics of Functions in $L_2$

M. Sh. Shabozov

Tajik National University, Dushanbe
Full-text PDF (479 kB) Citations (1)
References:
Abstract: Exact constants in Jackson–Stechkin type inequalities are found for the smoothness characteristics $\Lambda_m (f)$, $ m\in\mathbb N$, determined by averaging the norm of finite differences of $m$th order of functions $ f \in L_2$. A solution is given of the extremal problem of finding the supremum for best joint polynomial approximations of functions and their successive derivatives on some classes of functions from $L_2$ whose averaged norms of finite differences are bounded above by $1$.
Keywords: best approximations, upper bound, smoothness characteristic, finite differences.
Received: 10.01.2021
Revised: 02.06.2021
English version:
Mathematical Notes, 2021, Volume 110, Issue 3, Pages 432–439
DOI: https://doi.org/10.1134/S000143462109011X
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: M. Sh. Shabozov, “Inequalities between Best Polynomial Approximants and Smoothness Characteristics of Functions in $L_2$”, Mat. Zametki, 110:3 (2021), 450–458; Math. Notes, 110:3 (2021), 432–439
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm13005
  • https://www.mathnet.ru/eng/mzm/v110/i3/p450
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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