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

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

Abstract

We consider the generalized characteristics of smoothness of the functions $\omega^w(f, t)$ and $\Lambda^w(f, t), t > 0,$ in the space $L_2(R)$ and, on the classes $L^{\alpha}_2 (R)$ defined with the help of fractional-order derivatives $\alpha \in (0,\infty)$, obtain the exact Jackson-type inequalities for $\omega^w(f)$.
Published
25.09.2018
How to Cite
VakarchukS. B. “Generalized Characteristics of Smoothness and Some Extremе problems of the Approximation Theory of Functions in the Space $L_2 (R)$. I”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, no. 9, Sept. 2018, pp. 1166-91, http://umj.imath.kiev.ua/index.php/umj/article/view/1627.
Section
Research articles