In terms of the best approximations of functions and generalized moduli of smoothness, direct and inverse approximation theorems are proved for the Besicovitch almost periodic functions whose Fourier exponent sequences have a single limit point at infinity and their Orlicz norms are finite. Special attention is given to the study of cases where the constants in these theorems are unimprovable.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 5, pp. 701–716, May, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i5.7045.
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Chaichenko, S.O., Shidlich, A.L. & Shulyk, T.V. Direct and Inverse Approximation Theorems in the Besicovitch–Musielak–Orlicz Spaces of Almost Periodic Functions. Ukr Math J 74, 801–819 (2022). https://doi.org/10.1007/s11253-022-02102-5
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DOI: https://doi.org/10.1007/s11253-022-02102-5