TY - JOUR AU - S. O. Chaichenko PY - 2012/09/25 Y2 - 2024/03/30 TI - Best approximations of periodic functions in generalized lebesgue spaces JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 64 IS - 9 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2655 AB - 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. ER -