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Mean-Square “Angle” Approximation in the L2 Metric and the Values of Quasiwidths for Some Classes of Functions

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Ukrainian Mathematical Journal Aims and scope

In the metric L2, we establish exact inequalities, which relate the best approximations by trigonometric “angles” for the functions f(x, y) differentiable and 2𝜋-periodic in each variable to the integrals containing the moduli of continuity of higher order for mixed derivatives of these functions. For some classes of functions defined by the moduli of continuity, we determine the Kolmogorov and linear quasiwidths.

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Authors and Affiliations

  1. Tajikistan National University, Dushanbe, Tajikistan

    M. Sh. Shabozov

  2. Technological University of Tajikistan, Dushanbe, Tajikistan

    M. O. Akobirshoev

Authors
  1. M. Sh. Shabozov
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  2. M. O. Akobirshoev
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Correspondence to M. Sh. Shabozov.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 6, pp. 852–864, June, 2020. Ukrainian DOI: 10.37863/umzh.v72i6.1064.

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Shabozov, M.S., Akobirshoev, M.O. Mean-Square “Angle” Approximation in the L2 Metric and the Values of Quasiwidths for Some Classes of Functions. Ukr Math J 72, 990–1004 (2020). https://doi.org/10.1007/s11253-020-01837-3

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  • DOI: https://doi.org/10.1007/s11253-020-01837-3

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