On the exact values of mean $\nu$-widths of some classes of entire functions

We find the exact values of various $\nu$-widths for some classes of functions $f\in L_2^{(r)}(\mathbb R)$ differentiable on the axis $\mathbb R=(-\infty;+\infty)$ and satisfying the condition
$$\Bigg(\int_0^h\Omega_m^q(f^{(r)},t)\,dt\Bigg)^{1/q}\leq\Phi(h),$$
where $r,m\in\mathbb N$, $1/r<q\leq2$, $0<h\le\pi$, $\Omega_m(f^{(r)},t)_2$ is the generalized modulus of continuity of $m$th order of the derivative $f^{(r)}\in L_2(\mathbb R)$, and $\Phi(t)$ is an arbitrary continuous function increasing on $t\ge0$ and such that $\Phi(0)=0$.