Best polynomial approximations and widths of certain classes of functions in the space $L_2$

In the paper exact values of the $n$-widths are found for the class of differentiable periodic functions in the space $L_2[0,2\pi]$, satisfying the condition
$$ \left(\int^t_0\tau\Omega^{2/m}_m(f^{(r)},\tau)\,d\tau\right)^{m/2}\le\Phi(t), $$
where $0<t\le\pi/n$, $m,n,r\in\mathbb N$, $\Omega_m(f^{(r)},\tau)$ is the generalized modulus of continuity of order $m$ of the derivative $f^{(r)}\in L_2[0,2\pi]$, and $\Phi(t)$, $0\le t<\infty$ is a continuous non-decreasing function, such that $\Phi(0)=0$ and $\Phi(t)>0$ for $t>0$.