On the best polynomial approximation in the space L2 and widths of some classes of functions

  • S. B. Vakarchuk Днепропетр. ун-т им. А. Нобеля
  • V. I. Zabutnaya (Днепропетр. нац. ун-т)


We consider the problem of the best polynomial approximation of $2\pi$-periodic functions in the space $L_2$ in the case where the error of approximation $E_{n-1}(f)$ is estimated in terms of the $k$th-order modulus of continuity $\Omega_k(f)$ in which the Steklov operator $S_h f$ is used instead of the operator of translation $T_h f (x) = f(x + h)$. For the classes of functions defined using the indicated smoothness characteristic, we determine the exact values of different $n$-widths.
How to Cite
Vakarchuk, S. B., and V. I. Zabutnaya. “On the Best Polynomial Approximation in the Space L2 and Widths of Some Classes of Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 8, Aug. 2012, pp. 1025-32, https://umj.imath.kiev.ua/index.php/umj/article/view/2637.
Research articles