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

S. O.  Chaichenko; A. L. Shidlich; T. V.  Shulyk

doi:10.37863/umzh.v74i5.7045

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

DOI: https://doi.org/10.37863/umzh.v74i5.7045

Keywords: direct approximation theorem, inverse approximation theorem, Jackson type inequality, generalized module of smoothness

Abstract

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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