Generalized characteristics of smoothness and some extreme problems of the approximation theory of functions in the space $L_2 (R)$. II

  • S. B. Vakarchuk Днепропетр. ун-т им. А. Нобеля


In the second part of the paper, we establish the exact Jackson-type inequalities for the characteristic of smoothness $\Lambda^w$ on the classes of functions $L^{\alpha}_2 (R)$ defined by the fractional derivatives of order $\alpha \in (0,\infty )$ in the space $L_2(R)$. The exact values of the mean $\nu$ -widths for the classes of functions, defined by the generalized characteristics of smoothness $\omega w$ and $\Lambda w$ are also computed in $L_2(R)$.
How to Cite
Vakarchuk, S. B. “Generalized Characteristics of Smoothness and Some Extreme Problems of the approximation Theory of Functions in the Space $L_2 (R)$. II”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, no. 10, Oct. 2018, pp. 1345-73,
Research articles