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

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Matematicheskie Zametki, 2009, Volume 86, Issue 3, Pages 328–336
DOI: https://doi.org/10.4213/mzm3901 (Mi mzm3901)

This article is cited in 32 scientific papers (total in 32 papers)

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

S. B. Vakarchuk^a, V. I. Zabutnaya^b

^a Dnepropetrovsk University of Economics and Law
^b Dnepropetrovsk National University

Full-text PDF (472 kB) Citations (32)

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DOI: https://doi.org/10.4213/mzm3901

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.

Received: 18.06.2007

English version:
Mathematical Notes, 2009, Volume 86, Issue 3, Pages 306–313
DOI: https://doi.org/10.1134/S0001434609090028

Bibliographic databases:

UDC: 517.5

Language: Russian

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

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Linking options:

https://www.mathnet.ru/eng/mzm3901

https://doi.org/10.4213/mzm3901

https://www.mathnet.ru/eng/mzm/v86/i3/p328

This publication is cited in the following 32 articles:

Sergіi Vakarchuk, Valentina Zabutna, Mikhailo Vakarchuk, “Userednenі kharakteristiki gladkostі v $L_2$ ta otsіnki znachen poperechnikіv funktsіonalnikh klasіv”, Ukr. Mat. Zhurn., 77:2 (2025), 83
M. R. Langarshoev, “Nailuchshee priblizhenie analiticheskikh v edinichnom kruge funktsii v vesovom prostranstve Bergmana $\mathscr{B}_{2,\mu}$”, Vestnik rossiiskikh universitetov. Matematika, 29:145 (2024), 65–76
S. Vakarchuk, M. Vakarchuk, “Nablizhennya v serednomu sumami Fur'є–Besselya klasіv funktsіi u prostorі
L 2
[
( 0,1 )
; x ]
ta otsіnki znachen ïkh n -poperechnikіv”, Ukr. Mat. Zhurn., 76:2 (2024), 198
M. R. Langarshoev, A. G. Aidarmamadov, “Nailuchshee priblizhenie analiticheskikh v edinichnom kruge funktsii v vesovom prostranstve Bergmana”, Dalnevost. matem. zhurn., 24:1 (2024), 55–66
M. O. Akobirshoev, “O nailuchshem sovmestnom priblizhenii “uglom” v srednem periodicheskikh funktsii dvukh peremennykh iz nekotorykh klassov”, Izv. vuzov. Matem., 2024, no. 7, 24–36
Sergii Vakarchuk, Mykhailo Vakarchuk, “Approximation in the Mean for the Classes Of Functions in the Space L2[(0, 1); x] by The Fourier–Bessel Sums And Estimation of the Values of Their n-Widths”, Ukr Math J, 76:2 (2024), 214
M. O. Akobirshoev, “On the Best Simultaneous Angle Approximation in the Mean of Periodic Functions of Two Variables from Some Classes”, Russ Math., 68:7 (2024), 14
M. Sh. Shabozov, “On the Best Simultaneous Approximation in the Bergman Space $B_2$”, Math. Notes, 114:3 (2023), 377–386
Sergii B. Vakarchuk, “On estimates of diameter values of classes of functions in the weight space L2,γ (ℝ2), γ = exp(–x2 – y2)”, J Math Sci, 264:4 (2022), 471
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
M. R. Langarshoev, “O tochnykh znacheniyakh poperechnikov nekotorykh klassov funktsii iz $L_{2}$”, Dalnevost. matem. zhurn., 21:1 (2021), 61–70
M. Sh. Shabozov, G. A. Yusupov, D. D. Zargarov, “O nailuchshei sovmestnoi polinomialnoi approksimatsii funktsii i ikh proizvodnykh v prostranstve Khardi”, Tr. IMM UrO RAN, 27, no. 4, 2021, 239–254
Akgun R., “Mixed Modulus of Smoothness With Muckenhoupt Weights and Approximation By Angle”, Complex Var. Elliptic Equ., 64:2 (2019), 330–351
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
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
Sergei B. Vakarchuk, “Widths of some classes of functions defined by the generalized moduli of continuity ω
γ in the space L 2”, J Math Sci, 227:1 (2017), 105
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
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
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
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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