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)

Abstract

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.
Published
25.08.2012
How to Cite
VakarchukS. B., and ZabutnayaV. I. “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, http://umj.imath.kiev.ua/index.php/umj/article/view/2637.
Section
Research articles