Best approximations of periodic functions in generalized lebesgue spaces
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.