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Mat. Zametki, 1978, Volume 24, Issue 6, Pages 785–792 (Mi mz8265)  

This article is cited in 26 scientific papers (total in 26 papers)

Some inequalities between best approximations and moduli of continuity in an $L_2$ space

A. A. Ligun

Dneprodzerzhinsk Industrial Institute

Full text: PDF file (366 kB)

English version:
Mathematical Notes, 1978, 24:6, 917–921

Bibliographic databases:

UDC: 517.5
Received: 09.03.1977

Citation: A. A. Ligun, “Some inequalities between best approximations and moduli of continuity in an $L_2$ space”, Mat. Zametki, 24:6 (1978), 785–792; Math. Notes, 24:6 (1978), 917–921

Citation in format AMSBIB
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\pages 785--792
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\transl
\jour Math. Notes
\yr 1978
\vol 24
\issue 6
\pages 917--921
\crossref{https://doi.org/10.1007/BF01140019}
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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. S. B. Vakarchuk, “On Best Polynomial Approximations in $L_2$”, Math. Notes, 70:3 (2001), 300–310  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. S. B. Vakarchuk, “Jackson-Type Inequalities and Widths of Function Classes in $L_2$”, Math. Notes, 80:1 (2006), 11–18  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. M. Sh. Shabozov, “Widths of Classes of Periodic Differentiable Functions in the Space $L_{2}[0,2\pi]$”, Math. Notes, 87:4 (2010), 575–581  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Shabozov M.Sh., Yusupov G.A., “Inequalities between the Best Approximations and Homogenizations of Moduli of Continuity in the Space L-2”, Doklady Mathematics, 82:3 (2010), 892–895  crossref  isi
    5. Vakarchuk S.B., Doronin V.G., “BEST MEAN SQUARE APPROXIMATIONS BY ENTIRE FUNCTIONS OF FINITE DEGREE ON A STRAIGHT LINE AND EXACT VALUES OF MEAN WIDTHS OF FUNCTIONAL CLASSES”, Ukrainian Math J, 62:8 (2011), 1199–1212  crossref  isi
    6. M. Sh. Shabozov, G. A. Yusupov, “Best Polynomial Approximations in $L_2$ of Classes of $2\pi$-Periodic Functions and Exact Values of Their Widths”, Math. Notes, 90:5 (2011), 748–757  mathnet  crossref  crossref  mathscinet  isi
    7. 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
    8. Shabozov M.Sh. Yusupov G.A., “Widths of Certain Classes of Periodic Functions in l-2”, J. Approx. Theory, 164:7 (2012), 869–878  crossref  isi
    9. Shabozov M.Sh. Vakarchuk S.B., “On the Best Approximation of Periodic Functions by Trigonometric Polynomials and the Exact Values of Widths of Function Classes in l (2)”, Anal. Math., 38:2 (2012), 147–159  crossref  isi
    10. Yusupov G.A., “Tochnye neravenstva tipa dzheksona-stechkina i poperechniki funktsionalnykh klassov v $l_{2}$”, Izvestiya tulskogo gosudarstvennogo universiteta. estestvennye nauki, 2012, no. 2, 124–135  elib
    11. 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
    12. S. N. Vasil'ev, “Widths of some functional classes in the space $L_2$ on a period”, Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 202–207  mathnet  crossref  mathscinet  isi  elib
    13. Shabozov M.Sh. Vakarchuk S.B. Zabutnaya V.I., “Sharp Jackson-Stechkin Type Inequalities for Periodic Functions in l-2 and Widths of Function Classes”, Dokl. Math., 88:1 (2013), 478–481  crossref  isi
    14. 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
    15. 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
    16. S. B. Vakarchuk, “Best Mean-Square Approximations by Entire Functions of Exponential Type and Mean $\nu$-Widths of Classes of Functions on the Line”, Math. Notes, 96:6 (2014), 878–896  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    17. Vakarchuk S.B. Shvachko A.V., “On the Best Approximation in the Mean By Algebraic Polynomials With Weight and the Exact Values of Widths For the Classes of Functions”, Ukr. Math. J., 65:12 (2014), 1774–1792  crossref  isi
    18. 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
    19. 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
    20. Shabozov M.Sh., Palavonov K.K., “Exact Values of Widths of Certain Classes of Periodic Differentiable Functions in the Space l (2)[0, 2 Pi]”, Anal. Math., 41:1-2 (2015), 103–115  crossref  isi
    21. 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
    22. 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
    23. 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
    24. Shabozov M.Sh. Yusupov G.A. Temurbekova S.D., J. Approx. Theory, 215 (2017), 145–162  crossref  mathscinet  zmath  isi  elib  scopus
    25. 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
    26. 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
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