Widths of classes of periodic differentiable functions in the space L2[0, 2π]

We obtain exact values of different n-widths for classes of differentiable periodic functions in the space L2[0, 2π] satisfying the constraint \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left( {\int_0^h {\omega _m^p \left( {f^{\left( r \right)} ;t} \right)dt} } \right)^{{1 \mathord{\left/ {\vphantom {1 p}} \right. \kern-\nulldelimiterspace} p}} \leqslant \Phi \left( h \right) $$\end{document}, where 0 < h < ∞, 1/r < p ≤ 2, r ∈ ℕ, and ωm(f(r); t) is the modulus of continuity of mth order of the derivative f(r)(x) ∈ L2[0, 2π].