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Mat. Zametki, 2009, Volume 86, Issue 3, Pages 328–336 (Mi mz3901)  

This article is cited in 21 scientific papers (total in 21 papers)

A Sharp Inequality of Jackson–Stechkin type in $L_2$ and the Widths of Functional Classes

S. B. Vakarchuka, V. I. Zabutnayab

a Dnepropetrovsk University of Economics and Law
b Dnepropetrovsk National University

Abstract: We obtain sharp inequalities of Jackson–Stechkin type in which the modulus of continuity of the function is defined in terms of the Steklov function. For classes of functions given by this characteristic, we obtain sharp values of the $n$-widths.

Keywords: inequality of Jackson–Stechkin type, modulus of continuity, Fourier series, Steklov function, Bernstein $n$-width, Kolmogorov $n$-width, Gelfand $n$-width


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English version:
Mathematical Notes, 2009, 86:3, 306–313

Bibliographic databases:

UDC: 517.5
Received: 18.06.2007

Citation: S. B. Vakarchuk, V. I. Zabutnaya, “A Sharp Inequality of Jackson–Stechkin type in $L_2$ and the Widths of Functional Classes”, Mat. Zametki, 86:3 (2009), 328–336; Math. Notes, 86:3 (2009), 306–313

Citation in format AMSBIB
\by S.~B.~Vakarchuk, V.~I.~Zabutnaya
\paper A Sharp Inequality of Jackson--Stechkin type in~$L_2$ and the Widths of Functional Classes
\jour Mat. Zametki
\yr 2009
\vol 86
\issue 3
\pages 328--336
\jour Math. Notes
\yr 2009
\vol 86
\issue 3
\pages 306--313

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    This publication is cited in the following articles:
    1. M. Sh. Shabozov, G. A. Yusupov, “Exact constants in Jackson-type inequalities and exact values of the widths of some classes of functions in $L_2$”, Siberian Math. J., 52:6 (2011), 1124–1136  mathnet  crossref  mathscinet  isi
    2. S. B. Vakarchuk, V. I. Zabutnaya, “Jackson–Stechkin Type Inequalities for Special Moduli of Continuity and Widths of Function Classes in the Space $L_2$”, Math. Notes, 92:4 (2012), 458–472  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Yusupov G.A., “Tochnye neravenstva tipa dzheksona-stechkina i poperechniki funktsionalnykh klassov v $l_{2}$”, Izv. Tulskogo gos. un-ta. Estestvennye nauki, 2012, no. 2, 124–135  elib
    4. Vakarchuk S.B. Zabutnaya V.I., “On the best polynomial approximation in the space $L_2$ and widths of some classes of functions”, Ukr. Math. J., 64:8 (2013), 1168–1176  crossref  mathscinet  zmath  isi  scopus
    5. V. A. Abilov, M. V. Abilov, M. K. Kerimov, “Convergence rate estimates for spherical partial sums of double Fourier series”, Comput. Math. Math. Phys., 53:8 (2013), 1062–1069  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. M. Sh. Shabozov, K. Tukhliev, “Best Polynomial Approximations and the Widths of Function Classes in $L_{2}$”, Math. Notes, 94:6 (2013), 930–937  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. Temurbekova S.D., “Neravenstvo tipa Dzheksona-Stechkina dlya obobschennykh modulei nepreryvnosti i poperechniki nekotorykh funktsionalnykh klassov funktsii v prostranstve $L_2$”, Doklady Akademii nauk Respubliki Tadzhikistan, 56:4 (2013), 273–278  elib
    8. Tukhliev K., “O nailuchshem polinomialnom priblizhenii periodicheskikh funktsii v $L_2$ i poperechnikov nekotorykh klassov funktsii”, Doklady Akademii nauk Respubliki Tadzhikistan, 56:7 (2013), 515–520  elib
    9. S. B. Vakarchuk, “Mean Approximation of Functions on the Real Axis by Algebraic Polynomials with Chebyshev–Hermite Weight and Widths of Function Classes”, Math. Notes, 95:5 (2014), 599–614  mathnet  crossref  crossref  mathscinet  isi  elib
    10. M. R. Langarshoev, “Sharp inequality of Jackson–Stechkin type and widths of functional classes in the space $L_2$”, Eurasian Math. J., 5:1 (2014), 122–134  mathnet
    11. S. B. Vakarchuk, “Jackson-type inequalities for the special moduli of continuity on the entire real axis and the exact values of mean $\nu$-widths for the classes of functions in the space $L_2(\mathbb R)$”, Ukrainian Math. J., 66:6 (2014), 827–856  crossref  mathscinet  zmath  isi  scopus
    12. S. B. Vakarchuk, A. V. Shvachko, “On the best approximation in the mean by algebraic polynomials with weight and the exact values of widths for the classes of functions”, Ukrainian Math. J., 65:12 (2014), 1774–1792  crossref  mathscinet  zmath  isi  scopus
    13. G. A. Yusupov, “Inequalities of Jackson-Stechkin type and the values of widths for some classes of functions from $L_2$”, Anal. Math., 40:1 (2014), 69–81  crossref  mathscinet  zmath  isi  elib  scopus
    14. S. B. Vakarchuk, “Generalized Smoothness Characteristics in Jackson-Type Inequalities and Widths of Classes of Functions in $L_2$”, Math. Notes, 98:4 (2015), 572–588  mathnet  crossref  crossref  mathscinet  isi  elib
    15. S. B. Vakarchuk, V. I. Zabutnaya, “Inequalities between Best Polynomial Approximations and Some Smoothness Characteristics in the Space $L_2$ and Widths of Classes of Functions”, Math. Notes, 99:2 (2016), 222–242  mathnet  crossref  crossref  mathscinet  isi  elib
    16. Vakarchuk S.B., “Jackson-Type Inequalities with Generalized Modulus of Continuity and Exact Values of the n-Widths for the Classes of (?, ?)-Differentiable Functions in L 2. I”, Ukr. Math. J., 68:6 (2016), 823–848  crossref  mathscinet  isi  scopus
    17. Akgun R., “Mixed Modulus of Smoothness With Muckenhoupt Weights and Approximation By Angle”, Complex Var. Elliptic Equ., 64:2 (2019), 330–351  crossref  mathscinet  zmath  isi  scopus
    18. S. B. Vakarchuk, “Approximation by classical orthogonal polynomials with weight in spaces $L_{2,\gamma}(a,b)$ and widths of some functional classes”, Russian Math. (Iz. VUZ), 63:12 (2019), 32–44  mathnet  crossref  crossref  isi
    19. Vakarchuk S.B., “On the Estimates of Widths of the Classes of Functions Defined By the Generalized Moduli of Continuity and Majorants in the Weighted Space l-2,l-X(0,1)”, Ukr. Math. J., 71:2 (2019), 202–214  crossref  mathscinet  isi
    20. M. R. Langarshoev, S. S. Khorazmshoev, “Sharp inequalities of Jackson-Stechkin type and widths of classes of functions in $L_{2}$”, Ufa Math. J., 13:1 (2021), 56–67  mathnet  crossref  isi
    21. M. R. Langarshoev, “O tochnykh znacheniyakh poperechnikov nekotorykh klassov funktsii iz $L_{2}$”, Dalnevost. matem. zhurn., 21:1 (2021), 61–70  mathnet  crossref
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