  We find two-sided estimates for Kolmogorov, Bernstein, linear and projection
widths of the classes of convolutions of $2\pi$-periodic functions $\varphi$,
such that $\|\varphi\|_2\le1$, with fixed generated kernels
$\Psi_{\bar{\beta}}$, which have Fourier series of the form
$\sum\limits_{k=1}^\infty \psi(k)\cos(kt-\beta_k\pi/2), $ where $\psi(k)\ge0,$
$\sum\psi^2(k)<\infty, \beta_k\in\mathbb{R},$ in the space $C$. It is shown
that for rapidly decrising sequences $\psi(k)$ (in particular, if
$\lim\limits_{k\rightarrow\infty}{\psi(k+1)}/{\psi(k)}=0$) obtained estimates
are asymptotic equalities. We establish that asymptotic equalities for widths
of this classes are realized by trigonometric Fourier sums.
