Jackson-type inequalities with generalized modulus of continuity and exact values of the $n$-widths of the classes of $(ψ,β)$-differential functions in $L_2$. I

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


For the generalized moduli of continuity, including the ordinary moduli of continuity and various their modifications, we establish the exact constants for Jackson-type inequalities in the classes of $2\pi$ -periodic functions in the space $L_2$ with $(\psi , \beta)$-derivatives, introduced by Stepanets. These results take into account the classification of $(\psi , \beta)$-derivatives and enable us to consider the major part of Jackson-type inequalities obtained earlier in the classes of differentiable functions $L_2^r,\; r \in N$, from the common point of view.
How to Cite
Vakarchuk, S. B. “Jackson-Type Inequalities With Generalized Modulus of Continuity and Exact Values of the $n$-Widths of the Classes of $(ψ,β)$-Differential Functions in $L_2$. I”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, no. 6, June 2016, pp. 723-45, https://umj.imath.kiev.ua/index.php/umj/article/view/1874.
Research articles