In generalized Lebesgue spaces with variable exponent, we determine the orders of the best approximations in the classes of (ψ; β)-differentiable 2π-periodic functions, deduce an analog of the well-known Bernstein inequality for the (ψ; β)-derivative, and apply this inequality to prove the inverse theorems of approximation theory in these classes.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 9, pp. 1249–1265, September, 2012.
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Chaichenko, S.O. Best approximations of periodic functions in generalized lebesgue spaces. Ukr Math J 64, 1421–1439 (2013). https://doi.org/10.1007/s11253-013-0725-6
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DOI: https://doi.org/10.1007/s11253-013-0725-6