Direct and inverse approximation theorems in the Besicovitch – Musielak – Orlicz spaces of almost periodic functions

  • S. O. Chaichenko Donbas State Pedagog. Univ., Sloviansk, Donetsk region
  • A. L. Shidlich Inst. Math. Nat. Acad. Sci. Ukraine; Nat. Univ. Life and Environmental Sci. Ukraine, Kyiv
  • T. V. Shulyk Donbas State Pedagog. Univ., Sloviansk, Donetsk region
Keywords: direct approximation theorem, inverse approximation theorem, Jackson type inequality, generalized module of smoothness


UDC 517.5

In terms of the best approximations of functions and generalized moduli of smoothness, direct and inverse approximation theorems are proved for Besicovitch almost periodic functions whose Fourier exponent sequences have a single limit point in infinity and their Orlicz norms are finite. Special attention is paid to the study of cases when the constants in these theorems are unimprovable.


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How to Cite
Chaichenko , S. O., A. L. Shidlich, and T. V. Shulyk. “Direct and Inverse Approximation Theorems in the Besicovitch – Musielak – Orlicz Spaces of Almost Periodic Functions ”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 5, June 2022, pp. 701 -6, doi:10.37863/umzh.v74i5.7045.
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