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This article is cited in 21 scientific papers (total in 21 papers)
Jackson-Type Inequalities and Widths of Function Classes in $L_2$
S. B. Vakarchuk
Ukrainian Academy of Customs
Abstract:
The sharp Jackson-type inequalities obtained by Taikov in the space $L_2$ and containing the best approximation and the modulus of continuity of first order are generalized to moduli of continuity of $k$th order $(k=2,3,…)$. We also obtain exact values of the $n$-widths of the function classes $F(k,r,\Phi)$ and $\mathcal{F}_k^r (h)$, which are a generalization of the classes $F(1,r,\Phi)$ and $\mathcal{F}^r_1(h)$ studied by Taikov.
Keywords:
Jackson-type inequalities, width of function classes, modulus of continuity of $k$th order, periodic function, Bernstein, Kolmogorov, Gelfand $n$-widths
DOI:
https://doi.org/10.4213/mzm2774
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English version:
Mathematical Notes, 2006, 80:1, 11–18
Bibliographic databases:
    
UDC:
517.5
Received: 09.03.2005
Revised: 25.12.2005
Citation:
S. B. Vakarchuk, “Jackson-Type Inequalities and Widths of Function Classes in $L_2$”, Mat. Zametki, 80:1 (2006), 11–19; Math. Notes, 80:1 (2006), 11–18
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/mz2774https://doi.org/10.4213/mzm2774 http://mi.mathnet.ru/eng/mz/v80/i1/p11
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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
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Shabozov M.Sh. Yusupov G.A., “Widths of Certain Classes of Periodic Functions in l-2”, J. Approx. Theory, 164:7 (2012), 869–878
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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
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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
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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
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G. A. Yusupov, “Tochnye znacheniya poperechnikov nekotorykh klassov funktsii iz $L_2$ i minimizatsiya konstant v neravenstvakh tipa Dzheksona–Stechkina”, Model. i analiz inform. sistem, 20:5 (2013), 106–116
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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
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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
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