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This article is cited in 35 scientific papers (total in 35 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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm8890https://doi.org/10.4213/mzm8890 https://www.mathnet.ru/eng/mzm/v92/i4/p497
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