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Mat. Zametki, 2012, Volume 92, Issue 4, Pages 497–514 (Mi mz8890)  

This article is cited in 14 scientific papers (total in 14 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

DOI: https://doi.org/10.4213/mzm8890

Full text: PDF file (582 kB)
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English version:
Mathematical Notes, 2012, 92:4, 458–472

Bibliographic databases:

UDC: 517.538.5
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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. R. Langarshoev, “Tochnye neravenstva tipa Dzheksona–Stechkina i znacheniya poperechnikov nekotorykh klassov funktsii v prostranstve $L_{2}$”, Model. i analiz inform. sistem, 20:5 (2013), 90–105  mathnet
    2. Shabozov M.Sh., Oliftaev N.F., “Nailuchshie priblizheniya i tochnye znacheniya poperechnikov nekotorykh klassov periodicheskikh funktsii v $L_2$”, Izvestiya Akademii nauk Respubliki Tadzhikistan. Otdelenie fiziko-matematicheskikh, khimicheskikh, geologicheskikh i tekhnicheskikh nauk, 2013, no. 4(153), 23–32  elib
    3. 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 $L_2(\mathbb R)$”, Ukr. Math. J., 66:6 (2014), 827–856  crossref  mathscinet  zmath  isi  scopus
    4. K. Tukhliev, “O priblizhenii periodicheskikh funktsii v $L_2$ i znacheniyakh poperechnikov nekotorykh klassov funktsii”, Model. i analiz inform. sistem, 22:1 (2015), 127–143  mathnet  mathscinet  elib
    5. 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
    6. M. Sh. Shabozov, K. Tukhliev, “Neravenstva Dzheksona — Stechkina c obobschennymi modulyami nepreryvnosti i poperechniki nekotorykh klassov funktsii”, Tr. IMM UrO RAN, 21, no. 4, 2015, 292–308  mathnet  mathscinet  elib
    7. 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
    8. K. Tukhliev, “Nailuchshie priblizheniya i poperechniki nekotorykh klassov svertok v $L_{2}$”, Tr. IMM UrO RAN, 22, no. 4, 2016, 284–294  mathnet  crossref  mathscinet  elib
    9. S. B. Vakarchuk, “Jackson-type inequalities with a generalized modulus of continuity and exact values of $n$-widths of classes of $(\psi,\beta)$-differentiable functions in $L_2$. I”, Ukr. Math. J., 68:6 (2016), 823–848  crossref  mathscinet  isi  scopus
    10. S. B. Vakarchuk, “Jackson-type inequalities with a generalized modulus of continuity and exact values of $n$-widths of classes of $(\psi,\beta)$-differentiable functions in $L_2$. II”, Ukr. Math. J., 68:8 (2017), 1165–1183  crossref  mathscinet  isi  scopus
    11. M. Sh. Shabozov, M. S. Saidusajnov, “Upper Bounds for the Approximation of Certain Classes of Functions of a Complex Variable by Fourier Series in the Space $L_2$ and $n$-Widths”, Math. Notes, 103:4 (2018), 656–668  mathnet  crossref  crossref  isi  elib
    12. M. S. Saidusainov, “Analiz odnoi teoremy o neravenstve Dzheksona - Stechkina v prostranstve Bergmana $B_2$”, Tr. IMM UrO RAN, 24, no. 4, 2018, 217–224  mathnet  crossref  elib
    13. Babenko V.F. Konareva S.V., “Jackson-Stechkin-Type Inequalities For the Approximation of Elements of Hilbert Spaces”, Ukr. Math. J., 70:9 (2019), 1331–1344  crossref  isi
    14. M. Sh. Shabozov, A. A. Shabozova, “Nekotorye tochnye neravenstva tipa Dzheksona - Stechkina dlya periodicheskikh differentsiruemykh v smysle Veilya funktsii v $L_2$”, Tr. IMM UrO RAN, 25, no. 4, 2019, 255–264  mathnet  crossref  elib
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