Widths of functional classes defined by majorants of generalized moduli of smoothness in the spaces ${\mathcal S}^{p}$

  • F. Abdullayev Kyrgyz-Turkish Manas University, Bishkek, Kyrgyz republic; Mersin University, Mersin, Turkey
  • Anatolii Serdyuk Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
  • A. Shidlich Institute of mathematics, NAS of Ukraine
Keywords: Kolmogorov width, Bernstein width, best approximation, generelized module of smoothness, Jackson-type inequality

Abstract

UDC 517.5

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

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Published
18.06.2021
How to Cite
Abdullayev, F., A. Serdyuk, and A. Shidlich. “Widths of Functional Classes Defined by Majorants of Generalized Moduli of Smoothness in the Spaces ${\mathcal S}^{p}$”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 6, June 2021, pp. 723 -7, doi:10.37863/umzh.v73i6.6432.
Section
Research articles