2017
Том 69
№ 7

All Issues

Best approximations of periodic functions in generalized lebesgue spaces

Chaichenko S. O.

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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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