  We obtain the asymptotic equalities for the least upper bounds of
approximations by interpolation trigonometric polynomials with the equidistant
nodes $x_k^{(n-1)}=\frac{2k\pi}{2n-1},\ k\in\mathbb{Z},$ in metrics of the
spaces $L_p$ on classes of $2\pi$-periodic functions, representable as
convolutions of functions $\varphi, \ \varphi\perp1,$ which belongs to the unit
ball of the space $L_1$, and fixed generating kernels in the case where modules
of their Fourier coefficients $\psi(k)$ satisfy the condition
$\lim\limits_{k\rightarrow\infty} \psi(k+1)/\psi(k)=0.$ We obtain similar
estimates on the classes of $r$-differentiable functions $W^r_1$ for the
quickly increasing exponents of smoothness $r$ $(r/n\rightarrow\infty)$.
