Best approximations of periodic functions in generalized lebesgue spaces

• Date: 2012
• Main Authors: Chaichenko, S. O., Чайченко, С. О.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2012
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2655
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 wh...