$K$-Functionals and Exact Values of n-Widths of Certain Classes in the Spaces $C(2\pi )$ and $L_1(2\pi )$

For classes of $2\pi$-periodic functions whose $K$-functionals are majorized by functions satisfying certain constraints, exact values of Kolmogorov, Bernstein, and trigonometric $n$-widths in the spaces $C(2\pi )$ and $L_1(2\pi )$ are obtained. Examples of majorants that satisfy the requirements stated in this paper are given.