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Widths of Functional Classes Defined by the Majorants of Generalized Moduli of Smoothness in the Spaces \( {\mathcal{S}}^p \)

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Ukrainian Mathematical Journal Aims and scope

We obtain exact Jackson-type inequalities in terms of the best approximations and averaged values of the generalized moduli of smoothness in the spaces \( {\mathcal{S}}^p \). For classes of periodic functions defined by certain conditions imposed on the average values of the generalized moduli of smoothness, we determine the exact values of the Kolmogorov, Bernstein, linear, and projective widths in the spaces \( {\mathcal{S}}^p \).

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Authors and Affiliations

  1. “Manas” Kyrgyz–Turkish University, Bishkek, Kyrgyzstan

    F. G. Abdullayev

  2. Mersin University, Mersin, Turkey

    F. G. Abdullayev

  3. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    A. S. Serdyuk & A. L. Shidlich

Authors
  1. F. G. Abdullayev
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  2. A. S. Serdyuk
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  3. A. L. Shidlich
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Correspondence to F. G. Abdullayev.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 6, pp. 723–737, June, 2021. Ukrainian DOI: 10.37863/umzh.v73i6.6432.

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Abdullayev, F.G., Serdyuk, A.S. & Shidlich, A.L. Widths of Functional Classes Defined by the Majorants of Generalized Moduli of Smoothness in the Spaces \( {\mathcal{S}}^p \). Ukr Math J 73, 841–858 (2021). https://doi.org/10.1007/s11253-021-01963-6

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  • DOI: https://doi.org/10.1007/s11253-021-01963-6

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