TY - JOUR
AU - S. B. Vakarchuk
PY - 2016/06/25
Y2 - 2022/10/02
TI - 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
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 68
IS - 6
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1874
AB - 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.
ER -