Best approximations of periodic functions in generalized lebesgue spaces

  • S. O. Chaichenko Слов'ян. пед. ун-т


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.
How to Cite
ChaichenkoS. O. “Best Approximations of Periodic Functions in Generalized Lebesgue Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 9, Sept. 2012, pp. 1249-65,
Research articles