2017
Том 69
№ 9

# Best approximations of periodic functions in generalized lebesgue spaces

Chaichenko S. O.

Abstract

In generalized Lebesgue spaces with variable exponent, we determine the order of the best approximation on the classes of $(\psi, \beta)$-differentiable $2\pi$-periodic functions. We also obtain an analog of the well-known Bernstein inequality for the $(\psi, \beta)$-derivative, with the help of which the converse theorems of approximation theory are proved on the indicated classes.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 9, pp 1421-1439.

Citation Example: Chaichenko S. O. Best approximations of periodic functions in generalized lebesgue spaces // Ukr. Mat. Zh. - 2012. - 64, № 9. - pp. 1249-1265.

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