Best approximations of periodic functions in generalized lebesgue spaces

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

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.
Published
25.09.2012
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, http://umj.imath.kiev.ua/index.php/umj/article/view/2655.
Section
Research articles