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Matematicheskie Zametki, 2012, Volume 92, Issue 4, Pages 497–514
DOI: https://doi.org/10.4213/mzm8890 (Mi mzm8890) 		 
This article is cited in 32 scientific papers (total in 32 papers)

Jackson–Stechkin Type Inequalities for Special Moduli of Continuity and Widths of Function Classes in the Space $L_2$

S. B. Vakarchuka, V. I. Zabutnayab

a Dnepropetrovsk University of Economics and Law
b Dnepropetrovsk National University
Full-text PDF (582 kB) Citations (32)
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DOI: https://doi.org/10.4213/mzm8890
Abstract: We obtain sharp Jackson–Stechkin type inequalities for moduli of continuity of $k$th order $\Omega_k$ in which, instead of the shift operator $T_hf$, the Steklov operator $S_h(f)$ is used. Similar smoothness characteristic of functions were studied earlier in papers of Abilov, Abilova, Kokilashvili, and others. For classes of functions defined by these characteristics, we calculate the exact values of certain $n$-widths.
Keywords: Jackson–Stechkin type inequality, modulus of continuity, Steklov operator $S_h(f)$, $n$-width, Fourier series, Minkowski's inequality.
Received: 11.05.2010
Revised: 19.06.2011
English version:
Mathematical Notes, 2012, Volume 92, Issue 4, Pages 458–472
DOI: https://doi.org/10.1134/S0001434612090180
Bibliographic databases:
Document Type: Article
UDC: 517.538.5
Language: Russian
Citation: S. B. Vakarchuk, V. I. Zabutnaya, “Jackson–Stechkin Type Inequalities for Special Moduli of Continuity and Widths of Function Classes in the Space $L_2$”, Mat. Zametki, 92:4 (2012), 497–514; Math. Notes, 92:4 (2012), 458–472
Citation in format AMSBIB
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    • This publication is cited in the following 32 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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