  Using present a unified approach, we establish a Kolmogorov type comparison
theorem for the classes of $2\pi$-periodic functions defined by a special class
of operators having certain oscillation properties, which includes the
classical Sobolev class of functions with 2$\pi$-periodic, the Achieser class,
and the Hardy-Sobolev class as its special examples. Then, using these results,
we prove a Taikov type inequality, and calculate the exact values of
Kolmogorov, Gel$'$fand, linear and information $n$--widths of this class of
functions in some space $L_{q}$, which is the classical Lebesgue integral space
of 2$\pi$--periodic with the usual norm.
