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Mat. Zametki, 1976, Volume 20, Issue 3, Pages 433–438 (Mi mz7863)  

This article is cited in 36 scientific papers (total in 36 papers)

Reports read at the International Conference on the Theory of Approximation of Functions held at Kaluga from July 24 to 28, 1975

Inequalities containing best approximations and the modulus of continuity of functions in $L_2$

L. V. Taikov

Moscow Institute of Forestry Engineering

Full text: PDF file (344 kB)

English version:
Mathematical Notes, 1976, 20:3, 797–800

Bibliographic databases:

UDC: 517.5
Received: 12.02.1976

Citation: L. V. Taikov, “Inequalities containing best approximations and the modulus of continuity of functions in $L_2$”, Mat. Zametki, 20:3 (1976), 433–438; Math. Notes, 20:3 (1976), 797–800

Citation in format AMSBIB
\Bibitem{Tai76}
\by L.~V.~Taikov
\paper Inequalities containing best approximations and the modulus of continuity of functions in $L_2$
\jour Mat. Zametki
\yr 1976
\vol 20
\issue 3
\pages 433--438
\mathnet{http://mi.mathnet.ru/mz7863}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=427930}
\zmath{https://zbmath.org/?q=an:0343.42002}
\transl
\jour Math. Notes
\yr 1976
\vol 20
\issue 3
\pages 797--800
\crossref{https://doi.org/10.1007/BF01097254}


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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, “$K$-functionals and exact values of $n$-widths of some classes in $L_2$”, Math. Notes, 66:4 (1999), 404–408  mathnet  crossref  crossref  mathscinet  isi
    2. S. B. Vakarchuk, “On Best Polynomial Approximations in $L_2$”, Math. Notes, 70:3 (2001), 300–310  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. S. B. Vakarchuk, “Exact Constants in Jackson-type Inequalities and Exact Values of Widths”, Math. Notes, 78:5 (2005), 735–739  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. 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
    5. V. S. Balaganskii, “Exact constant in the Jackson–Stechkin inequality in the space $L^2$ on the period”, Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S78–S102  mathnet  crossref  isi  elib
    6. Shabozov, MS, “On exact values of quasiwidths for some classes of differentiable periodic functions of two variables”, Ukrainian Mathematical Journal, 61:6 (2009), 1013  crossref  isi
    7. S. B. Vakarchuk, V. I. Zabutnaya, “A Sharp Inequality of Jackson–Stechkin type in $L_2$ and the Widths of Functional Classes”, Math. Notes, 86:3 (2009), 306–313  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. 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
    9. 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
    10. 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
    11. 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
    12. Li J. Liu Y.-p. Su Ch.-M., “The Jackson Inequality and Widths of Function Classes in l-2([0,1], X(2V+1))”, J. Complex., 28:5-6 (2012), 582–596  crossref  isi
    13. 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
    14. Shabozov M.Sh., “Exact Jackson-Stechkin-Type Inequalities for 2 Pi-Periodic Functions in (2) and Widths of Some Classes of Functions”, Ukr. Math. J., 63:10 (2012), 1633–1639  crossref  isi
    15. 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
    16. 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
    17. 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  isi
    18. 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
    19. G. A. Yusupov, “Best polynomial approximations and widths of certain classes of functions in the space $L_2$”, Eurasian Math. J., 4:3 (2013), 120–126  mathnet
    20. 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
    21. 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
    22. 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
    23. 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
    24. 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
    25. 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
    26. Yusupov G.A., “Jackson's-Stechkin's Inequality and the Values of Widths For Some Classes of Functions From $L_2$”, Anal. Math., 40:1 (2014), 69–81  crossref  isi
    27. 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
    28. 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
    29. 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
    30. 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
    31. 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
    32. 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
    33. Shabozov M.Sh. Yusupov G.A. Temurbekova S.D., J. Approx. Theory, 215 (2017), 145–162  crossref  mathscinet  zmath  isi  elib  scopus
    34. Vakarchuk S.B., “On the Moduli of Continuity and Fractional-Order Derivatives in the Problems of Best Mean-Square Approximation By Entire Functions of the Exponential Type on the Entire Real Axis”, Ukr. Math. J., 69:5 (2017), 696–724  crossref  isi
    35. 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
    36. 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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