2018
Том 70
№ 12

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

Vakarchuk S. B.

Abstract

In the space $L_2$, we determine the exact values of some $n$-widths for the classes of functions such that the generalized moduli of continuity of their $(\psi, \beta)$ - derivatives or their averages with weight do not exceed the values of the majorants $\Phi$ satisfying certain conditions. Specific examples of realization of the obtained results are also analyzed.

Citation Example: Vakarchuk S. B. Jackson-type inequalities with generalized modulus of continuity and exact values of the $n$-widths of the classes of $(ψ,β)$-differentiable functions in $L_2$. II // Ukr. Mat. Zh. - 2016. - 68, № 8. - pp. 1021-1036.